We will start with an introduction to p-adic automorphic forms and then discuss a variant of the q-expansion principle (called the Serre-Tate expansion principle) for p-adic automorphic forms on unitary groups of arbitrary signature. We outline how this can be used to produce p-adic families of automorphic forms on unitary groups, which has applications to the construction of p-adic L-functions. This is done via an explicit description of the action of certain differential operators on the Serre-Tate expansion. Speaker(s): Jessica Fintzen (University of Michigan)