The most general supersymmetric theories involving eight supercharges can only be off-shell if one introduces an auxiliary manifold associated with the R-symmetry group. The resulting structure, which can be formulated either as projective or harmonic superspace, naturally provides a framework for constructing hypermultiplet actions both in flat space and in supergravity. I will discuss recent progress in unifying these two approaches and describe how the covariant approach to supergravity in projective superspace naturally yields a corresponding covariant harmonic formulation.