Keg, -hd, 4 bytes

./÷

Try it online!

Splits on dots, and prints the last element.

Pip, 10 bytes

@RV(q^".")

Splits on dots, gets first element of reverse. I wish I could make this work without the parentheses.

Try it online!

8086 Assembly (NASM) + DOS, 262 bytes source, 50 bytes assembled

I'm pretty new to assembly, but I thought I'd give this a try. This is a full DOS program, not just a snippet.

section .bss
b resb 256
org 256
section .text
mov byte[b],254
mov ah,10
mov dx,b
int 33
mov bh,0
mov bl,[b+1]
add bx,b+2
mov bp,bx
l:sub bx,1
cmp byte[bx],46
jne l
mov byte[bx],10
p:mov ah,2
mov dl,[bx]
int 33
add bx,1
cmp bx,bp
jb p
int 32

Essentially, it reads a line of text into a buffer, seeks the end, then seeks backwards until it reaches a .. Then it just prints the rest of the string from that point on. I wasn't able to use DOS's built-in print function, though, since that uses $ as the end-of-string character, which the prompt says is a valid character for the extension itself.

Here is the hexdump of the assembled binary:

00000000  c6 06 34 01 fe 88 e4 ba  34 01 cd 21 b7 00 8a 1e
00000010  35 01 81 c3 36 01 89 dd  83 eb 01 80 3f 2e 75 f8
00000020  c6 07 0a b4 02 8a 17 cd  21 83 c3 01 39 eb 72 f3
00000030  cd 20

Python3 (32 bytes)

f=input()
print(f[f.rfind('.'):])

Try it online!

APL (Dyalog Unicode), 10 bytes (SBCS)

⊃∘⌽'.'∘≠⊆⊢

-7 bytes after Bubbler's suggestion.

Try it online!

APL (Dyalog Unicode), 17 bytes (SBCS)

⊃⌽'.'(1↓¨,⊂⍨⊣=,)⍞

Explanation

⊃⌽'.'(1↓¨,⊂⍨⊣=,)⍞
                ⍞ string input
            ⊣=,)  get characters, evaluate if they are equal to the left arg '.'
         ,⊂⍨      enclose each part after a dot
  '.'(1↓¨         drop each dot in the strings
 ⌽                reverse the split string array
⊃                 take the first value

Try it online!

Arn, 6 bytes

Ê^!⁺╔d

Try it!

Explained

Unpacked: :!".":}

    _ Variable initialized to STDIN; implied
  :! Split on
    "." String containing a period
:} Tail

Setanta, 66 34 bytes

gniomh(s){toradh roinn@s(".")[-1]}

Try it here!

brainfuck, 45 bytes

,[>,]>+[[-]++[<->------]<---<[->+>+<<]>]>[.>]

Try it online!

33 v1.0, 13 bytes

The behaviour of the y operator was changed in v1.1, so this program no longer works

Gets the file name passed as an argument and prints the extension (without leading '.') to standard output.

1bt'.'ywmcbtp

Explanation:

1b            (Gets the second item in argv, the filename input)
  t'.'y       (Splits that by '.')
       wmcb   (Gets the last element in the list)
           tp (Prints to standard output)

Forth (gforth), 45 bytes

: f begin 1 -1 d+ s" ."search 0= until type ;

Try it online!

Code Explanation

: f               start a new word definition
  begin           start an indefinite loop
    1 -1 d+       remove the first character from the string
    s" ."search   find the length and starting address of the first substring that starts with '.'
    0=            check if '.' was found in the string
  until           end the loop if not
  type            output the result
;                 end the word definition
 

Befunge-98 (FBBI), 50 bytes

{v
 >~:a`!#v_
--2*86:$<:u-10_v#
02-u0}>:#,_@   >00

Try it online!

Puts string onto stack, then iterates through it in reverse, putting each new character onto new stack. Once a . is encountered, discard original stack and output new stack in 0gnirts format.

Perl 6, 11 bytes

{m/.w+$/}

Try it online!

Brain-Flak, 76 bytes

{((((([()()()]){}){}){}()){}{}<>)<>}<>{({}(((()()()()()){}()){}()){}<>)<>}<>

Try it online!

Explanation:

{          loop over stack
  (                            push
    (((([()()()]){}){}){}()){} -46
  {}                           plus the top of the stack
  <>)                          to the other side
<>}        retuen for more

<>      on the other side...

{       loop until 0
  (                             push
     {}                         the top of the stack
     (((()()()()()){}()){}()){} +46
  <>)                           to the first side
<>}       return for more

<> print the first side

6 bytes less than the other Brain-Flack solution.

Turing Machine But Way Worse, 1315 1287 bytes

0 0 0 1 1 0 0
1 0 1 1 8 0 0
0 1 0 1 2 0 0
1 1 1 1 9 0 0
0 2 0 1 3 0 0
1 2 1 1 a 0 0
0 3 0 1 4 0 0
1 3 1 1 b 0 0
0 4 0 1 5 0 0
1 4 1 1 c 0 0
0 5 0 1 6 0 0
1 5 1 1 d 0 0
0 6 0 1 7 0 0
1 6 1 1 e 0 0
0 7 0 1 f 0 0
1 7 1 1 0 0 0
0 8 0 1 9 0 0
1 8 1 1 9 0 0
0 9 0 1 a 0 0
1 9 1 1 a 0 0
0 a 0 1 b 0 0
1 a 1 1 b 0 0
0 b 0 1 c 0 0
1 b 1 1 c 0 0
0 c 0 1 d 0 0
1 c 1 1 d 0 0
0 d 0 1 e 0 0
1 d 1 1 e 0 0
0 e 0 1 0 0 0
1 e 1 1 0 0 0
0 f 0 0 g 0 0
1 f 1 0 g 0 0
0 g 0 0 h 0 0
1 g 1 0 p 0 0
0 h 0 0 q 0 0
1 h 1 0 i 0 0
0 i 0 0 r 0 0
1 i 1 0 j 0 0
0 j 0 0 s 0 0
1 j 1 0 k 0 0
0 k 0 0 l 0 0
1 k 1 0 t 0 0
0 l 0 0 u 0 0
1 l 1 0 m 0 0
0 m 0 0 n 0 0
1 m 1 0 v 0 0
0 n 0 0 o 0 0
1 n 1 0 g 0 0
0 p 0 0 q 0 0
1 p 1 0 q 0 0
0 q 0 0 r 0 0
1 q 1 0 r 0 0
0 r 0 0 s 0 0
1 r 1 0 s 0 0
0 s 0 0 t 0 0
1 s 1 0 t 0 0
0 t 0 0 u 0 0
1 t 1 0 u 0 0
0 u 0 0 f 0 0
1 u 1 0 f 0 0
0 o 0 1 w 0 0
1 o 1 1 w 0 0
0 w 0 1 x 0 0
1 w 1 1 E 0 0
0 x 0 1 y 0 0
1 x 1 1 F 0 0
0 y 0 1 z 0 0
1 y 1 1 G 0 0
0 z 0 1 A 0 0
1 z 1 1 H 0 0
0 A 0 1 B 0 0
1 A 1 1 I 0 0
0 B 0 1 C 0 0
1 B 1 1 J 0 0
0 C 0 1 D 0 0
1 C 1 1 K 0 0
0 D 0 1 D 0 1
1 D 1 1 w 1 0
0 E 0 1 F 0 0
1 E 1 1 F 0 0
0 F 0 1 G 0 0
1 F 1 1 G 0 0
0 G 0 1 H 0 0
1 G 1 1 H 0 0
0 H 0 1 I 0 0
1 H 1 1 I 0 0
0 I 0 1 J 0 0
1 I 1 1 J 0 0
0 J 0 1 K 0 0
1 J 1 1 K 0 0
0 K 0 1 w 1 0
1 K 1 1 w 1 0

Try it online!

Wow, this is big.

Pushy, 13 bytes

K46-$v;F@46+"

Try it online!

                Implicit: string on stack as character codes
K46-            Subtract 46 from each code point, mapping '.' to 0
    $v;         While the top of stack is non-zero, move to auxiliary stack
       F        Copy auxiliary stack onto main stack
        @       Reverse (to obtain original order)
         46+    Add 46 (to obtain original characters)
            "   Print as a string.  

Emacs, 6 bytes

The cursor needs to be at the start of the line containing the string.

This will delete the entire line if there's no extension.

C-<SPC> C-e C-r . <RET> <BACKSPACE>

Explanation:

C-<SPC>      start a selection
C-e          go to the end of the line
C-r . <RET>  search for "." backward
<BACKSPACE>  delete the selected text (which should be the text before the last ".")

Pepe, 48 bytes

rEeeEeEEEeREEeREEEerEEREEEEEEEreererEEEEeEeereee

Try it online!

Red 9 bytes

Suffix? f

Assumes file is is in word 'f

MBASIC, 129 bytes

1 INPUT F$:F=INSTR(F$,"."):IF F=0 THEN END
2 FOR I=LEN(F$) TO 1 STEP -1:P$=MID$(F$,I,1):O$=P$+O$:IF P$="." THEN PRINT O$:END
3 NEXT

Explanation

Get a filename. If it doesn't contain a period, bail out. Otherwise, collect letters from right to left to build an output string. When we see a period, print the string.

Output

? hi.txt
.txt

? .bashrc
.bashrc

? [email protected][]h
.h0wC[]h

R, 40 26 bytes

-14 bytes thanks to J.Doe

sub("^.*[.]","",scan(,""))

Try it online!

PowerShell, 34 26 bytes

-8 bytes thanks to @mazzy

(Read-Host).Split('.')[-1]

Takes input from STDIN. Actually managed to golf it down shorter than the built-in.

PowerShell, 20 bytes

($args-split'.')[-1]

Takes input from commandline arguments. Big thanks to @mazzy again!

PowerShell (with built-in), 36 bytes

[IO.Path]::GetExtension((Read-Host))

C++, 73 bytes

I'm a bit surprised that no one tried C++, since it's an easy one :

#include<string>
auto e=[](std::string s){return s.substr(s.rfind(46));};

And the code to test ( may have to iostream, initializer_list, and exception ) :

std::initializer_list<std::string> test{
    "hi.txt", // .txt
    "carrot.meme", // .meme
    "lol", // invalid string position
    "what..is..this..file", // .file
    ".bashrc", // .bashrc
    "[email protected][]h", // .h0wC[]h
    "agent.000" // .000
};

for (const auto& a : test) {
    try {
        std::cout << e(a) << 'n';
    }
    catch (std::out_of_range& r) {
        std::cout << "out of range exception : " << r.what() << 'n';
    }
}

And, as you may expect, like compilers, if there's undefined behavior, there's no undefined behavior. If there's no file extension, the function will throw a std::out_of_range exception, as said in cppreference

V, 4 bytes

òdt.

Try it online!

Recursively delete everything up to, but not including the next .

Kotlin, 17 bytes

split(".").last()

Beautified

split(".").last()

Test

data class Test(val input: String, val output: String)

val test = listOf(
        Test("hi.txt", "txt"),
        Test("carrot.meme", "meme"),
        Test("what..is..this..file", "file"),
        Test(".bashrc", "bashrc"),
        Test("[email protected][]h", "h0wC[]h"),
        Test("agent.000", "000")
)

fun String.f() =
split(".").last()

fun main(args: Array<String>) {
    for ((i, o) in test) {
        if (o != i.f()) {
            throw AssertionError()
        }
    }
}

TIO

TryItOnline

Jotlin, 17 bytes

split(".").last()

Full file:

data class Test(val input: String, val output: String)

val test = listOf(
        Test("hi.txt", "txt"),
        Test("carrot.meme", "meme"),
        Test("what..is..this..file", "file"),
        Test(".bashrc", "bashrc"),
        Test("[email protected][]h", "h0wC[]h"),
        Test("agent.000", "000")
)

fun String.f() = split(".").last()

for ((i, o) in test) {
    if (o != i.f()) {
        throw AssertionError()
    }
}

Funky, 26 bytes

s=>(k=s::split".")[(#k)-1]

Try it online!

SmileBASIC, 45 bytes

INPUT S$@L
E$=POP(S$)+E$ON"."==E$[0]GOTO@L?E$

Outputs extension with the period.

Taxi, 1397 bytes

Go to Post Office:w 1 l 1 r 1 l.Pickup a passenger going to Chop Suey.Go to Chop Suey:n 1 r 1 l 4 r 1 l.[a]Pickup a passenger going to Narrow Path Park.Go to Narrow Path Park:n 1 l 1 r 1 l.Go to Chop Suey:e 1 r 1 l 1 r.Switch to plan "b" if no one is waiting.Switch to plan "a".[b]Go to The Babelfishery:n 1 l 1 l.[c]Go to Fueler Up:n.Go to Joyless Park:n 2 r.Go to Narrow Path Park:w 1 r 3 l.Pickup a passenger going to Cyclone.Go to Cyclone:w 1 l 1 r 2 l.Pickup a passenger going to Crime Lab.Pickup a passenger going to Joyless Park.'.' is waiting at Writer's Depot.Go to Writer's Depot:s.Pickup a passenger going to Crime Lab.Go to Crime Lab:n 1 r 2 r 2 l.Switch to plan "c" if no one is waiting.Go to Narrow Path Park:n 5 l.[d]Pickup a passenger going to Chop Suey.Go to Chop Suey:e 1 r 1 l 1 r.Go to Narrow Path Park:n 1 l 1 r 1 l.Switch to plan "e" if no one is waiting.Switch to plan "d".[e]Go to Joyless Park:e 1 r 3 l.Switch to plan "f" if no one is waiting.Pickup a passenger going to Narrow Path Park.Go to Fueler Up:w 1 l.Go to Narrow Path Park:n 4 l.Switch to plan "e".[f]Go to Narrow Path Park:w 1 r 3 l.[g]Switch to plan "h" if no one is waiting.Pickup a passenger going to KonKat's.Go to KonKat's:e 1 r.Pickup a passenger going to KonKat's.Go to Narrow Path Park:n 2 l.Switch to plan "g".[h]Go to KonKat's:e 1 r.Pickup a passenger going to Post Office.Go to Post Office:s 3 r 1 l.

Try it online!

Taxi doesn't have a reverse function so this ballooned pretty quickly. The logic is:

1. Break the string into characters
2. Reverse the array
3. Iterate through each until a period is found, storing each in a FIFO array
4. Empty the array (because there's only one LIFO array available)
5. Dump the FIFO array into the LIFO array
6. Concatenate the LIFO array and output

FORTRAN 90, 87 bytes

CHARACTER(99)F,L
READ*,F;DO I=1,LEN(F)
IF(F(I:I)=='.')L=F(I:LEN(F))
ENDDO
PRINT*,L
END

A shorter version in FORTRAN 90.

FORTRAN 77, 137 bytes

      PROGRAMC;IMPLICITCHARACTER*99(F)
      READ*,F;DOI=LEN(F),1,-1;IF(F(I:I).EQ.'.')THEN
      PRINT*,F(I:LEN(F));EXIT;ENDIF;ENDDO;END

There is no space in PROGRAM C, nor in IMPLICIT CHARACTER. It works (!) in gfortran, but I'm not sure it works in others compilers. The program takes input from stdin and outputs the extension with the period. The total length of the file name is limited by 99.

SNOBOL4 (CSNOBOL4), 46 bytes

	I =INPUT
S	I '.' REM . I	:S(S)
	OUTPUT =I
END

Try it online!

Takes the input, then repeatedly replaces it with all the text following the first . until no .s remain, then outputs the value.

C# (Visual C# Interactive Compiler), 22 bytes

s=>s.Split('.').Last()

Implicit using System.Linq; FTW!

Try it online!

Python 3, 46 bytes

-8 bytes thanks to Wheat Wizard and Scrooble

import sys
print(sys.argv[1].split('.')[-1])

EDIT: I fixed the code, and the filename is a command-line argument

T-SQL, 48 bytes

SELECT RIGHT(F,CHARINDEX('.',REVERSE(F))) FROM T

SQL Fiddle

Stax, 4 bytes

'./H

Run and debug online!

Explanation

Split on ., take last part.

><>, 18 bytes

i:0(6$.:"."=?]
ro|

Try it online!

How It Works:

i:(6$.  Jump to the second line if out of input
      :"."=  Else check if the character is a .
           ?[ And create a new stack if it is
              Loop back to the beginning of the line
If it is end of input
ro|  Reverse the current stack once and output, erroring on the EOF (-1)

JavaScript, 21 bytes

x=>x.split('.').pop()

Explanation:

This code takes x.txt and turns it into a array. The last element of the array is the file type. This code uses the pop function to remove the last element. In the process, the pop function returns the last element.

Aceto, 6 bytes

r'.:Qp

Try it online!

r       grabs input as string
 '.     literal period
   :    split string on period
    Q   grap bottom item
     p  print it

Add++, 9 bytes

L,"."$tbU

Try it online!

CJam, 6 bytes

q'./W=

Try it online!

        Print
    W     the last
     =    element
   /      of the result of splitting
q         the input
 '.       on the character '.'

ActionScript 2.0, 42 bytes

function a(b){trace(b.split(".").pop());};

Technically the ;s aren't required for it to compile, at least in JPEXS, but it's good practice. Call:

a("a.b");

(traces "b")

><>, 50 bytes

i:0( ?v
v[:<2~<
r  ^]+1r<
>:"."=?v^
v?l<r~r<;
>o ^

Try it online!

Vim, 5 bytes

$F.d0

Explanation: find last . in line, delete everything before it

Another, longer, but in my opinion still interesting approach with 9 bytes (notice the trailing new line)

d/.*./e

This one works similarly, 5 bytes (again, trailing new line):

d?.

Google Sheets, 25 bytes

An anonymous worksheet function that takes input from cell A1 and outputs the detected file extension of the form Extension to the calling cell.

=RegexExtract(A1,"[^.]+$

Yabasic, 34 bytes

A basic answer

Takes input as a string from STDIN, and outputs of the form .Extension to STDOUT.

Input""s$
?Mid$(s$,RInStr(s$,"."))

Try it online!

Excel VBA, 29 bytes

An anonymous VBE immediate window function that takes input via cell [A1] and outputs to the console. Return string is of the form .Extension.

?Mid([A1],InStrRev([A1],"."))

Excel, 58 bytes

=TRIM(RIGHT(SUBSTITUTE(A1,".",REPT(" ",LEN(A1))),LEN(A1)))

Perl 5, 8 bytes

7 bytes code + 1 for -p.

s;.*.;

Try it online!

Ohm v2, 5 bytes

I..ï⁾

Try it online!

K (oK), 6 bytes

Solution:

*|"."

Try it online!

Examples:

*|".""whats.up.txt"
"txt"
  *|".""[email protected][]h"
"h0wC[]h"

Explanation:

Split the input on ".", reverse | this list, and then take the first * one. K is interpreted right-to-left:

*|"." / the solution
  "." / "." split (),
 |     / reverse
*      / first

Ruby, 16 bytes

->s{s[/[^.]+$/]}

Try it online!

Julia, 22 bytes

g(n)=split(n,'.')[end]

Tcl, 21 bytes

puts [file ext $argv]

Try it online!

Cheddar, 16 bytes

@.sub(/.*./,"")

simple regex solution. Alternative solution using split:

@.split('.')[-1]

C (gcc), 77 60 52 bytes

char*f(char*s){for(s+=strlen(s);*--s-46;);return s;}

Try it online!

-17 bytes from Jonathan Frech

-8 bytes by removing i and doing arithmetic on s directly

Ungolfed (same strategy):

char *extension(char *original) {
    original = original + strlen(original);
    while(original[0] != '.') --original;
    return original;
}

Haskell, 32 30 29 bytes

-1 byte thanks to Laikoni

r=reverse
r.fst.span(/='.').r

self-explanatory

Lua, 53 30 bytes

Replaces everything upto the last . with the empty string ''.

Double parenthesis to select only the first return value of gsub.

Any golfing tips are welcome, I'm rusty in lua...

print(((...):gsub('.*%.','')))

Try it online!

C#, 35 bytes

s=>s.Substring(s.LastIndexOf("."));

Try it online!

REXX 53

parse value reverse(arg(1)) with e "." 
say reverse(e)

Pyth, 5 bytes

ecz.

try it here

Awk, 14 13 characters

(10 9 characters code + 4 characters command line option.)

{$0=$NF}1

Thanks to:

• Robert Benson for spotting the unnecessary semicolon (-1 character)

Sample run:

bash-4.4$ awk -F. '{$0=$NF}1' <<< $'hi.txtncarrot.memenlolnwhat..is..this..filen.bashrcnT00M@n3KaPZ.h0wC[]h'
txt
meme
lol
file
bashrc
h0wC[]h

C#, 47 34 27 bytes

System.IO.Path.GetExtension

Saved 6 bytes thanks to @totallyhuman.

Try it online!

Octave, 24 bytes

@(x)strsplit(x,'.'){end}

Creates an anonymous function named ans which can accept a string as input

Online Demo

MATL, 8 7 bytes

46&YbO)

Try it at MATL Online!

Explanation

        % Implicitly grab input as string
46      % ASCII for '.'
&Yb     % Split the input string at the '.' characters
O)      % Retrieve just the last part
        % Implicitly print the result

Gema, 3 characters

*.=

Sample run:

bash-4.4$ gema '*.=' <<< 'what..is..this..file'
file

jq, 15 14 characters

(11 10 characters code + 4 characters command line options.)

./"."|last

Sample run:

bash-4.4$ jq -Rr './"."|last' <<< 'what..is..this..file'
file

On-line test

Java 8, 52 27 bytes

s->s.replaceAll(".*\.","")

Try it here.

Replace everything before the last dot (and the dot itself) with nothing.

This is shorter than using split (s->s.split("\.")[s.split("\.").length-1];) or substring (s->s.substring(s.lastIndexOf('.'));).

Batch, 10 bytes

@echo %~x1

Strangely competitive for once.

GNU Make, 12 bytes

$(suffix $1)

Not using a builtin, 27 bytes:

$(lastword $(subst ., ,$1))

C#, 33 41 bytes

a=>a.Split('.').Last();

Edit as suggested:

using System.Linq;a=>a.Split('.').Last();

Charcoal, 6 4 bytes

-2 bytes thanks to Erik the Outgolfer

⊟⪪Ｓ.

Try it online!

Explanation

⊟      Pop
  ⪪ .  Split on "."
   Ｓ  Next input as string
       Implicit print of value

Common Lisp, 57 bytes

(lambda(s)(#1=reverse(subseq #2=(#1# s)0(search"."#2#))))

Try it online (added some bytes to call this anonymous function and display returned string)

Explanation

(#1=reverse ...)     ;reverse is now accessible with #1# - saves 1 byte. I 
                     ;also need to reverse output of function inside to 
                     ;get extension in correct order
#2=(#1# s)           ;reverse of input string is now accessible with #2#
(search"."#2#)       ;I take reversed string and search for "." to get position of 
                     ;first instance of "." in string from the end of it
(subseq ... 0 ...)   ;get part of reversed string, 
                     ;starting from first character and ending just 
                     ;before first occurance of "."
                     ;this gives reversed extension

I get substring of reversed string, starting from 0, ending on this

Javascript (ES5), 38 bytes

function(s){return s.split(".").pop()}

c function, 21

• 1 byte saved thanks to @Dennis.
• 3 bytes saved thanks to @JohanduToit.
• 2 bytes saved thanks to @Neil.
• 1 byte saved thanks to @algmyr.

f(s){s=rindex(s,46);}

Try it online.

Japt, 3 bytes

2 bytes of code, +1 for the h flag.

q.

Explanation:

q.       Split the input by `.`
   -h    Return the last item

Try it online!

Japt, 6 5 bytes

q'. o

Try it online!

Explanation

 q'. o
Uq'. o
Uq'.    # Split the input at "."
     o # Return the last item

Ruby, 21 bytes

->f{f.split('.')[-1]}

12 bytes

File.extname

JavaScript (ES6), 19 bytes

Returns the full filename when there's no file extension. I suppose this is an acceptable undefined behavior.

let f =

s=>s.split`.`.pop()

console.log(f("hi.txt"))               // -> txt
console.log(f("carrot.meme"))          // -> meme
console.log(f("lol"))                  // -> undefined behavior
console.log(f("what..is..this..file")) // -> file
console.log(f("[email protected][]h")) // -> h0wC[]h
console.log(f(".bashrc")) // -> bashrc

Groovy, 37 bytes

{it.substring(it.lastIndexOf(".")+1)}

Mathematica, 13 22 bytes

Edit: Not sure how I missed the ".bashrc" test case. Thanks to Artyer for keeping me honest.

FileExtension["a"<>#]&

If the input matches .[^.]+, then FileExtension just returns the empty string, so we prepend the letter a. In any other case, prepending a doesn't affect output of FileExtension.

Go, 85 bytes

Go is... troublesome.

import(."fmt"
."os"
."strings")
func main(){s:=Split(Args[1],".");Print(s[len(s)-1])}

Try it online!

A sample of parentheses from the code:

()(){([])([()])}

Pure bash, 13

echo ${1##*.}

Try it online.

Brain-Flak, 84 bytes

Includes +2 for -rc

(()){{}([((((()()()){}())()){}{}){}]({}<>)<>)({()(<{}>)}{})}{}{{}}<>{}{({}<>)<>}<>

Try it online!

# Push 1 to start the loop
(())

# Start loop
{{}

  # If TOS == 46 i.e. '.'
  ([((((()()()){}())()){}{}){}]({}<>)<>)({()(<{}>)}{})
  # ^------------------------^ ^-------^ 
  #           This is 46         Also, copy TOS to other stack

# End loop after the first '.'
}{}

# Delete everything from this stack
{{}}

# Delete the '.' that got copied
<>{}

# Copy everything back to reverse it to the correct order
{({}<>)<>}<>

Neo4j Cypher, 24 bytes

return split($i,".")[-1]

Input is in a param (i), probably the only way for cypher to take input. Pretty straightforward. Cypher has never been used on PPCG before

V, 5, 3 bytes

Since more of this answer is unprintable than printable, here is a hexdump:

00000000: cd81 ae                                  ...

Try it online!

This uses Jan Dvorak's algorithm, it just happens to be a more efficient encoding of it.

Explanation:

Í       " Remove all occurrences of:
 0x81   "   Anything (greedy)
     ®  "   Followed by a dot 

Old solution:

$T.d|

Retina, 5 bytes

.*.

Replaces everything and a dot with nothing at all.

Try it online!

Python 2, 25 bytes

lambda s:s.split('.')[-1]

Try it online!

sed, 8 bytes

s:.*.::

Try it online!

PHP, 21 Bytes

<?=pathinfo($argn,4);

Try it online!

is a shorter expression for

<?=pathinfo($argn)[extension];

pathinfo

PHP, 27 Bytes

<?=end(explode(".",$argn));

explode

Try it online!

PHP <7.0, 26 Bytes

<?=end(split(".",$argn));

deprecated split

Jelly, 4 bytes

ṣ”.Ṫ

A monadic link taking the file name and returning the extension with no leading ..

Try it online!

How?

Literally does what was asked...

ṣ”.Ṫ - Main link: list of characters, f
 ”.  - literal '.'
ṣ    - split f at occurrences of '.'
   Ṫ - tail (get the last chunk)

05AB1E, 4 bytes

'.¡¤

Try it online! or Try All Tests

'.   # Push '.'
  ¡  # Split on occurrences of '.'
   ¤ # Tail

JavaScript (ES6), 33 31 28 bytes

s=>s.slice(s.lastIndexOf`.`)

Spec change in comments removes the need for +1.

-3 bytes thanks to nderscore

JS (ES6), 26 25 bytes

x=>/.([^.]+)$/.exec(x)[1]

-1 byte thanks to Shaggy

document.querySelector('pre').innerText = (x=>/.([^.]+)$/.exec(x)[1])("example.txt")

<input oninput = "document.querySelector('pre').innerText = (x=>x.match(/.([^.]+)$/)[1])(this.value)" value = "example.txt">
<pre></pre>

Alternate, 29 bytes:

x=>(y=x.split`.`)[y.length-1]