Using random matrix theory, Keating and Snaith conjectured that central values of L-functions in families should have a log-normal distribution with a prescribed mean and variance based on the symmetry type of the family. Due to the recent work of Radziwiłł and Soundararajan, we obtain the conjectured lower bound for cubic Hecke L-functions over the Eisenstein field. In this talk, we will discuss this result and the history of the connection between L-functions and random matrices. This is joint work with Peng-Jie Wong.