Yes

The Minecraft world is 256 blocks (as of Minecraft 1.2) from top to bottom. The reason for the height restriction is that the Minecraft world is made of 16x16x256 'chunks'. These are loaded into memory and rendered starting with the ones closest to the player. A 3D world of chunks (where the world is 'infinite' vertically as well as horizontally) is a whole lot more complex than a 2D world of chunks to manage, and optimizing for smooth gameplay would be a challenge. 256 is a convenient number that's a power of 2 (making it align nicely in memory).

Note that there is also a separate build height on servers. In the server.properties file, there is a property max-build-height which defaults to 256. Server admins can lower this value to prevent players placing blocks above a certain height, but it will not prevent natural terrain from spawning above this level, or players climbing natural structures above this height.

Although it is theoretically possible for a mod to increase the height limit of the map, I can't find any that work with the current version of Minecraft or are in active development.

The height in unmodded Minecraft is restricted. From the bottom of the world to the highest possible point is 256 meters, or blocks.

If you want to build very high, build in the nether... That way you have plenty of space to go... Infinity. But in the over world, in order to build to infinity you need mods. The reason why there is a height limit is because the terrain would generate way to high, and the computer would lag or buffer and crash. The x and y dimensions also have a limit. 30,000,000 both sides. However, again, I have a question? Can't mojang set two height limits? One for the terrain, which is 256, or 512 and the building which is infinity?

You can go 256 blocks above in the overworld, but in the nether, there is bedrock above and underneath the nether.

if you play in the snapshot 20w49a you can get blocks placed at a y-coordinate from 500 to -500 but it is buggy and requires a datapack like this: https://github.com/onnowhere/examples

As of 21w06a the build height has changed, it is now from y=-64 to y=320. 64 blocks have been added to both the top and bottom of the world, since this is still a snapshot this is subject to change. The total build height is now 384 blocks and can be modified using datapacks.