The hypermultiplet moduli space \(M_H\) in type II string theories compactified on a Calabi-Yau threefold \(X\) is largely constrained by supersymmetry (which demands quaternion-Kählerity), S-duality (which requires an isometric action of \(SL(2, \mathbb{Z})\)) and regularity. Mathematically, \(M_H\) ought to encode all generalized Donaldson-Thomas invariants on \(X\) consistently with wall-crossing, modularity and homological mirror symmetry. We review recent progress towards computing the exact metric on \(M_H\), or rather the exact complex contact structure on its twistor space.