Einstein´s theory of gravitation, known as general relativity (GR), is nearly a century old but continues to inspire new developments in mathematics, particularly in geometric analysis. Without assuming any physics, I will give a brief overview of the main ideas behind GR with an emphasis on geometry. One theme will be how physical, non-rigorous arguments can lead to geometric conjectures, and ultimately theorems. Time permitting, I will discuss some recent work on global consequences of nonnegative scalar curvature.