The twisted doubling method (joint work with Friedberg, Ginzburg, and Kaplan) gives an integral representation for the tensor product L-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. This can be viewed as a generalization of the doubling integrals of Piatetski-Shapiro and Rallis. In this talk, we explain how to describe the doubling integrals in a conceptual setting.