Attached to a newform f of weight 2 and an imaginary quadratic field K, the Kummer images of Heegner points give rise to an anticyclotomic Euler System for the p-adic Galois representation associated with f. In this talk I will try to explain, assuming that the prime p splits in K, how the extension by Ben Howard of this construction to Hida families can be seen as producing a two-variable p-adic L-function in the spirit of Perrin-Riou. In the weight variable, we can thus show that Howard's construction interpolates the étale Abel-Jacobi images of Heegner cycles; in the anticyclotomic variable, this leads to new cases of the Bloch-Kato conjecture. The extension of some of these results to general CM fields in which p splits completely seems to be within reach.