Twists of supersymmetric field theories have been the source of an enormous amount of new mathematics, including (just for example) Seiberg-Witten theory and mirror symmetry. It is reasonable to expect that twists of supergravity theories will exhibit even richer structure, but they remain comparatively unexplored, largely due to their intricacy. For example, a holomorphically twisted version of the AdS/CFT correspondence was proposed by Kevin Costello and Si Li, motivated by constructions in topological string theory and the work of Bershadsky-Cecotti-Ooguri-Vafa; Costello and Li conjectured a connection between their version of BCOV theory and the type IIB supergravity theory, but did not verify this connection directly. I will show that the pure spinor superfield technique, which has been known for some time in the physics literature, can be used to elegantly and economically construct supersymmetric theories, as well as to swiftly compute their twists. In each case, the resulting structures are governed by the classical algebraic geometry of certain affine varieties. If time permits, I'll discuss the examples of type IIB supergravity and eleven-dimensional supergravity in some detail.