the aim of this talk is to introduce the audience to the halpern-lauchli theorem, which is a ramsey-theoretic statement about products of trees. we will discuss several applications of the theorem and outline a number of different proofs. while the original proof was combinatorial in nature, there are now a number of proofs that interact with ideas from set-theoretic forcing. one of these proofs is new, and is joint work with chris lambie-hanson.