The goal of this talk is to explain what the rank of a normal function is and to sketch a proof that the rank of the normal function of the genus g Ceresa cycle is 3g-3 provided g > 2. I will review the basics of normal functions and then sketch a proof of the result. The motivation comes from work of Ziyang Gao and Shou-Wu Zhang on the Arakelov theory of moduli spaces of curves. I understand that Gao has given an independent proof of the rank result using Ax-Schanuel.