I will discuss  a joint work with Angenent, Brendle and Daskalopoulos in which we show that all 3d closed rotationally symmetric ancient solutions to Ricci flow have the same asymptotics and we precisely describe those. After that I will show how we use this to prove that the only 3d closed noncollapsed ancient solutions to Ricci flow are the round spheres and Perelman's solutions. The latter look like a cylinder in the middle, which is capped off by two caps that look like Bryant steady solitons.

The classification result is a joint work with Brendle and Daskalopoulos.