Cosmic inflation is an impressively successful paradigm in our understanding of the early Universe. Its embedding into particle physics is however still an open question. In this talk, I will present a `complete' particle physics model of inflation. Based on the implementation of D-term hybrid inflation in strongly coupled supersymmetric gauge theories, this setup overcomes all the usual problems of D-term hybrid inflation, including the consistent generation of an Fayet-Iliopoulos term in supergravity and the cosmic string problem. The D term may be associated with a gauged U(1)_B-L, so that the end of inflation spontaneously breaks B-L in the visible sector, setting the stage for neutrino mass generation and leptogenesis.