I have a paintbrush made with plastic bristles. But the most common form of art brush is probably:

wooden handle, with a metal wrapper round the end to hold the hair bristles in place

The handle: Wood or plastic in combination with metal to hold the bristles.
Bristle: Hairs from different animals and fibre from plants. Plastic of different types.

http://en.wikipedia.org/wiki/Brush

Badger and Squirrel hairs are the most commonly used animal bristles.

Badger for their stiffness (for impasto painting and large areas.

Squirrel for flexibiliuty and softness - ideal for detail and watercolours etc.

Plastics are cheaper - probably nylon or something similar.

What the cheap Chinese brushes on the market use I dread to think!

Rathr than use yet more plastic, why don't they collect human hair from hairdressers and use that?