Asymptotic Formulas for Moments of L-functions

I will discuss the classical problem of estimating moments of L-functions in families with emphasis on those L-functions coming from automorphic forms. Given an upper bound on a moment of L-functions, I will describe a technique for refining the given estimate to an asymptotic formula. These formulas have applications to ranks of elliptic curves, Fourier coefficients of 1/2 integral weight modular forms, integral points on ellipsoids, and subconvex estimates for individual L-functions.