Modern extracellular recording technologies now enable simultaneous recording from large numbers of neurons. This has driven the development of new statistical models for analyzing and interpreting neural population activity. Here we provide a broad overview of recent developments in this area. We compare and contrast different approaches, highlight strengths and limitations, and discuss biological and mechanistic insights that these methods provide. While still an area of active development, there are already a number of powerful models for interpreting large scale neural recordings even in complex experimental settings.