a solution to a geometric flow is called ancient if it has a backhistory going back infinitely far in time. ancient solutions of parabolic pde are analogous to entire solutions of elliptic pde. in particular, they play a fundamental role in understanding singularity formation. \\ \\ perelman studied ancient solutions to the ricci flow in dimension 3 which are kappa-noncollapsed, and proved a crucial structure theorem for these ancient kappa-solutions. moreover, perelman conjectured that, up to scaling, every noncompact ancient kappa-solution in dimension 3 is isometric to either the bryant soliton or the standard cylinder (or a quotient thereof). in these lectures, i will discuss the proof of this conjecture.