What is A^1-homotopy theory?

Under the name A^1-homotopy theory, Fabien Morel and Vladimir Voevodsky imported methods from algebraic topology to algebraic geometry and algebraic K-theory. One of its first successful applications was Voevodsky's solution of the Milnor conjectures relating Galois cohomology and quadratic forms over fields of characteristic not two. This talk will provide an introduction to the subject, with a focus on the main idea that the affine line A^1 can be used to parametrize homotopies of algebraic objects.