abstract: We explain how Heegner points on Shimura curves can be used to study the Iwasawa theory of a rational elliptic curve $E$ over anticyclotomic $\mathbb Zp$-extensions of imaginary quadratic fields, where $p$ is a prime of supersingular reduction for $E$. This is based on joint work (partly in progress) with Mirela Ciperiani (Austin) and Matteo Longo (Padova).