Abstract: The premise of massive gravity is deceptively simple - adding a mass term to the graviton action. Yet it was only in 2010 that a permissible non-linear massive gravity Lagrangian, now known as the dRGT Lagrangian, was first written down. Since then, dRGT theory has generated considerable interest, but many fundamental questions about it remain unanswered. In this talk, I will review the motivations and long history of massive gravity, before moving on to discuss some of our recent progress on understanding its dynamics. We shall learn how to study the characteristics of the massive graviton, seeing that the familiar helicity-2 components remain on the usual light cone. We will then put dRGT on a computer, and marvel at the complicated things that happen when we try to model perhaps the simplest gravitational phenomenon: spherical collapse. Most of the time, the result will turn out to look very different from a standard GR black hole.