The Erdos-Szekeres conjecture is a well-known conjecture in Ramsey theory and discrete combinatorics. In 1935, Erdos and Szekeres proved the following: for any positive integer N, there is a number f(N) such that f(N) points in the plane in general position has a subset of N points that forms the vertices of a convex polygon. Until this year, the tightest known upper bound for f(N) was O(4^N / N^(1/2)). In 2016, Andrew Suk nearly settled the conjecture by announcing a proof showing $f(N) = O(2^(N + o(N))$. I will outline the main ideas of Andrew Suk's proof. Speaker(s): Jineon Baek (University of Michigan)