The rings Z and F_q[T] share many properties in common, so one might try to study number theory over F_q[T]. A (global) function field is a finite extension of F_q(T), just as a number field is a finite extension of Q. In this talk I will discuss the function field analogy. In particular, we will sketch a proof of an analogue of the ABC conjecture and Fermat’s last theorem in function fields.