Neutrino Mass Models

The discovery of nonzero neutrino masses is among the most important particle physics results of the last two decades: It indicates that the Standard Model of particle physics is incomplete. After 20 years of intense experimental and theoretical research, we still do not know the physics that leads to nonzero neutrino masses. The purpose of this review is to discuss the different models for nonzero neutrino masses. In doing so, I describe the differences between the models, how they connect to other aspects of particle physics, and whether or how one can hope to establish which model- if any-is a faithful description of nature.