Who doesn't like one of these three: geometry, topology, and combinatorics? Sperner's lemma, a combinatorial statement that is equivalent to the Brouwer fixed point theorem in topology, is amazing and powerful. I'll explain why, give heartwarming old and new proofs, and present some generalizations to polytopes that has surprised me with diverse applications: to the study of triangulations, to fair division problems, and the Game of Hex.