The Gross-Kohnen-Zagier theorem states that certain generating series of Heegner points on a Shimura curve are modular forms of weight $3/2$ valued in its Jacobian. We will explain this theorem and outline a new approach to prove it using the theory of $p$-adic uniformization and $p$-adic families of theta series of half-integral weight. This is joint work with Lea Beneish, Henri Darmon, and Lennart Gehrmann.