The low energy effective couplings of four-dimensional N = 2 supersymmetric gauge theory to topological invariants of the background gravitational field play an important role in the study of topology of four-manifolds, in the computation of central charges of N = 2 superconformal theories, and in the study of M5-branes in string theory. In this talk, I will review the historical developments and previous conjectures, and then I will show how to determine these effective gravitational couplings from a first-principle calculation. This talk is based on my joint work with Jan Manschot and Gregory Moore.