The neural ideal was introduced by Curto, Itskov, et al in 2013 to study the firing patterns of a set of neurons (called a neural code), turning problems in neuroscience and coding theory into algebraic questions. In this talk I will give an overview of neural ideals, describe a simple criterion for determining whether a neural ideal is in canonical form, and describe how Betti numbers and regularity can help us classify neural ideals. This work is joint with Hugh Geller and Nora Youngs.