Abstract: The theory of Heegner points, and more generally Heegner cycles, allows one to build special cohomology classes attached to twists of modular forms by Hecke characters of imaginary quadratic fields. The aim of this talk is to study how these vary in p-adic families: I will explain how to construct a 2-parameter p-adic analytic family of cohomology classes, attached to a Coleman family of modular forms and a choice of quadratic field, which interpolates the Heegner classes for all classical specialisations of the Coleman family and all possible Hecke characters unramified outside p. This is joint a joint project with Dimitar Jetchev and Sarah Zerbes.