A local system on a (punctured) curve is called rigid if its isomorphism class is determined by the isomorphism classes of its local monodromy. Perhaps the most famous such local system is the sheaf of solutions to the Gaussian hypergeometric equation. Studying rigidity of this equation dates back to Riemann who used considerations about monodromy to derive quadratic transformations for hypergeometric functions. In this talk I will explain the notion of rigidity for local systems and its role in the geometric Langlands program via rigid automorphic data.