How come we can grow nanowires? Semiconductors

It is a difficult question, since there exist many types of nanostructures, largely depending on the techniques used to fabricate them. I will cite a few, without giving particular focus to nanowires:

• Molecular beam epitaxy is a well established technique for fabricating computer chips. It is widely used for creating two-dimensional semiconductor structures (two-dimensional electron gas), which can be further fashioned into any shape (dots, wires, etc.) by depositing metallic gates on the top of the structure and applying negative potential to them (split-gate technique).
• Self-assembly or colloidal techniques: a thin layer is deposited on a substrate semiconductor of different type. Due to the material properties mismatch, boundary effects, etc., the layer collapses and forms small drops or strips, i.e. quantum dots or quantum wires.
• Molecular self-assembly molecules/atoms from a gas phase crystallize on a seeded substrate in a form of columns. Depending on the height of such a column, it will be either a dot or a wire.
• Atomic deposition One could simply deposit a chain of atoms (i.e., gold atoms) to form a wire.
• Carbon nanotubes and fullerene buckyballs are naturally made quantum wires and quantum dots (although the methods for their synthesis may resemble molecular self-assembly).
• Finally, one could simply suspend a molecule or a chain of molecules between electrodes.

Disclaimer: This is by no means a complete list. Moreover, being a theorist I am probably rather sloppy in terminology and descriptions.