When your equations are too complicated, sometimes you have to just make up new ones. Einstein taught us that the speed of light is absolute, which means space and time should be joined in a single geometric object called spacetime. He also showed how gravity can be understood as the curvature of this geometry. However, in all but the most ideal situations, it’s extremely hard to solve Einstein’s equations for gravity. In this talk, I will motivate and introduce tools for interpolating between Einstein’s gravity and good old-fashioned Newtonian physics using ‘Newton-Cartan’ spacetime geometry. While some of these concepts have been known for a long time, they have recently been dusted off and modernized. This was motivated in part by new and exciting results in string theory and holography, where these methods can help us to understand previously-inaccessible corners of the complicated full theory, as I will briefly mention at the end of the talk.