A family of permutations is 2-intersecting if any two permutations agree on at least 2 points. Ellis, Friedgut and Pilpel showed that for large enough n, such families contain at most (n-2)! permutations, and Ellis characterized the extremal families. Meagher and Razafimahatratra extended this to all n, but were unable to characterize the extremal families. Using ideas borrowed from theoretical computer science, we characterize the extremal families. Joint work with Gilad Chase, Neta Dafni, Noam Lifshitz, Nathan Lindzey, and Marc Vinyals.