Abstract: Quantum curves have been introduced by physicists to capture quantum invariants defined by a topological quantum field theory. A mathematical theory describes a quantum curve as a certain family of holonomic D-modules on an algebraic curve. An effective perturbative construction of quantum curves is desired. Topological recursion is an algorithmic procedure for constructing a certain family of meromorphic symmetric multidifferentials. Conjecturally, topological recursion quantises a classical spectral curve, decorated with some extra data, by calculating the all-order asymptotic expansion of a corresponding quantum curve. Specifically, for the Hitchin spectral curve, topological recursion may be interpreted as geometric quantisation of the holomorphic cotangent bundle. I will describe some basic definitions and examples, and report on the current understanding of the theory.