In the first part of my talk, I will present a general classification of Riemannian three-manifolds on which one can put 3d N=2 supersymmetric field theories while preserving some amount of supersymmetry. This formalism clarifies the relationship between the extra couplings necessary to preserve supersymmetry in curved space, on the one hand, and various operators of the flat space theory, on the other hand. In the second part of the talk I will present some simple applications of this formalism. In particular I will present exact results for various two-point functions of N=2 SCFTs which were hitherto out of reach.