We give a definitional framework for point-function obfuscation in which security is parameterized by a class of algorithms we call target generators. Existing and new notions are captured and explained as corresponding to different choices of this class. This leads to an elegant question: Is it possible to provide a generic construction, meaning one that takes an arbitrary class of target generators and returns a point-function obfuscator secure for it? We answer this in the affirmative with three generic constructions, the first based on indistinguishability obfuscation, the second on deterministic public-key encryption and the third on universal computational extractors. By exploiting known constructions of the primitives assumed, we obtain new pointfunction obfuscators, including many under standard assumptions. We end with a broader look that relates different known and possible notions of point function obfuscation to each other and to ours. 1 Department of Computer Science & Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA. Email: firstname.lastname@example.org. URL: http://cseweb.ucsd.edu/~mihir/. Supported in part by NSF grants CNS-1116800, CNS-1228890 and CNS-1526801. This work was done in part while the author was visiting the Simons Institute for the Theory of Computing, supported by the Simons Foundation and by the DIMACS/Simons Collaboration in Cryptography through NSF grant CNS-1523467. 2 Department of Computer Science & Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, USA. Email: email@example.com. Supported in part by NSF grants CNS-1116800 and CNS-1228890.