We associate to any matroid a motivic zeta function. If the matroid is representable by a complex hyperplane arrangement, then thiscoincides with the motivic Igusa zeta function of the arrangement.Although the motivic zeta function is a valuative invariant which is finer than the characteristic polynomial, it is not obvious how one should extract meaningful combinatorial data from the motivic zeta function. One strategy is to specialize to the topological zeta function. I will survey what is known about these functions and discuss some open questions.