One of Erdős's greatest contributions to geometry was his problem on distinct distances that asks: what is the least number of distinct distances among $N$ points in the plane? This seemingly innocent question inspired many other related questions, such as the Erdős unit distance problem, which asks: how often can a particular distance at most arise among $N$ points? In this talk we will recount the history of these classic questions and then focus on some variants, such as angles, chains and triangles, that have seen recent progress.