I’ll discuss limits and differential invariants of normal functions: how they relate to the Ceresa cycle on M_3; and how they predict families of cycles (some known, some unknown) over other moduli spaces. The main computation is a classification of infinitesimal normal functions over locally symmetric varieties (begun with R. Keast, and recently extended with X. Cheng and W. Li). I will discuss its implications for cycles on abelian varieties and for special subvarieties in the Torelli locus.