Joyce structures and their twistor spaces

Joyce structures are a class of geometric structures which first arose in relation to holomorphic generating functions for Donaldson-Thomas invariants. They can be thought of as non-linear analogues of Frobenius structures, or as special classes of complex hyperkähler manifolds. We give a detailed introduction to Joyce structures, with particular focus on the geometry of the associated twistor space. We also prove several new results.