We introduce the notion of adaptive trapdoor functions (ATDFs); roughly, ATDFs remain one-way even when the adversary is given access to an inversion oracle. Our main application is the black-box construction of chosenciphertext secure public-key encryption (CCA-secure PKE). Namely, we give a black-boxconstructionofCCA-SecurePKEfromATDFs,aswell asaconstruction of ATDFs from correlation-secure TDFs introduced by Rosen and Segev (TCC ’09). Moreover, byanextension ofarecentresultofVahlis (TCC’10), we show that ATDFs are strictly weaker than the latter (in a black-box sense). Thus, adaptivity appears to be the weakest condition on a TDF currently known to yield the first implication. We also give a black-box construction of CCA-secure PKE from a natural extension of ATDFs we call tag-based ATDFs that, when applied to our constructions of the latter from either correlation-secure TDFs, or lossy TDFs introduced by Peikert and Waters (STOC ’08), yield precisely the CCA-secure PKE schemes in these works. This helps to unify and clarify their schemes. Finally, we show how to realize tag-based ATDFs from an assumption on RSA inversion not known to yield correlation-secure TDFs.