Let p = p_1 ... p_n be a permutation in the symmetric group S_n written as a sequence. The descent set of p is the set of indices i such that p_i > p_{i+1}. A classic result of MacMahon states the the number of permutations in S_n with a given descent set is a polynomial in n. But little work seems to have been done concerning the properties of these polynomials. The peak set of p is the set of indices i such that p_{i+1} < p_i > p_{i+1}. Recently Billey, Burdzy, and Sagan proved that the number of permutations in S_n with given peak set is a polynomial in n times a power of two. I will survey what is known about these two polynomials, including their degrees, roots, coefficients, and analogues for other Coxeter groups.