The problem of giving exact formulas for the number of lattice points in a convex polytope has interested mathematicians for many years. Pick’s Formula (c. 1890) gives the answer in dimension two, and in the 1960s, Ehrhart achieved interesting results in higher dimensions. In the past fifteen years, much progress has been made using the tool of toric varieties. Recent toric results of Brion, Morelli, Khovanskii, Vergne, and the speaker have helped us understand the lattice point question much more clearly. In addition, there is a close link between the number theory which arises in these formulas (Dedekind sums and their generalizations) and special values of zeta functions. In particular, this link provides a new conceptual understanding of formulas of Shintani and Zagier (70’s) that express values of zeta functions of real quadratic fields at negative integers.