This talk discusses a class of supersymmetric models of inflation, in which minimal supersymmetric standard model (MSSM) is coupled renormalisably to minimal F-term inflation. This constitutes a minimal renormalisable extension of the MSSM which has the ingredients for a satisfactory cosmology, including explanations for inflation, dark matter, neutrino masses and baryogenesis. Such models can exit inflation to a vacuum characterised by large Higgs vevs, whose vacuum energy is controlled by supersymmetry-breaking. Given an unstable large-Higgs vacuum, the true ground state is reached after a period of thermal inflation at a scale of around $10^9$ GeV, which solves several cosmological problems of the F-term inflation scenario.