Abstract: Beginning with the basics of pointwise ergodic theory, I will discuss my forthcoming proof of the Furstenberg conjecture, on the pointwise convergence of the bilinear ergodic averages, 1/N sum_{n \leq N} T^n f T^{n^2} g,] where f,g in L^{infty}(X)] are bounded functions on a probability space (X,mu), and T:X to X is a measure-preserving transformation. Joint work with Mariusz Mirek (Rutgers) and Terence Tao (UCLA).