Recent advances of analysis on the hypercube have found some surprising applications in Banach space theory, computational learning theory, random graphs, and social choice. I will present several examples including Enflo's problem, Talagrand's inequality, and learning low-degree functions: how many values of an unknown function f on n boolean inputs one needs to know in order to efficiently approximate the function? The talk is based on joint works with D. Beltran, A. Eskenazis, R. van Handel, J. Madrid, Y. Stone, and A. Volberg.