Abstract: It was originally noticed by Dwork in the 1960s that p-adic solutions of certain differential equations (those arising as Picard-Fuchs equations of families of algebraic varieties) can be used to explicitly describe the zeta functions of varieties over finite fields. This observation has recently become the basis for algorithms to compute these zeta functions; in order to prove correctness of these algorithms, one must give explicit bounds for the convergence of solutions of certain p-adic differential equations. Some such bounds were given by Christol, Dwork, and Robba; we will describe some recent improvements.