A self-similar group (G,X) consists of a group G acting faithfully on a homogeneous rooted tree such that the action satisfies a self-similarity condition. In this talk I'll outline a generalisation of Nekrashevych's theorem that K-theoretic invariants of associated C*-algebras satisfy Poincaré duality. This result ties together ideas from operator algebras, dynamical systems and geometric group theory. This is joint work with Nathan Brownlowe, Alcides Buss, Daniel Gonçalves, Jeremy Hume, and Aidan Sims.