  No-scale supergravity provides a successful framework for Starobinsky-like
inflation models. Two classes of models can be distinguished depending on the
identification of the inflaton with the volume modulus, $T$ (C-models), or a
matter-like field, $\phi$ (WZ-models). When supersymmetry is broken, the
inflationary potential may be perturbed, placing restrictions on the form and
scale of the supersymmetry breaking sector. We consider both types of
inflationary models in the context of high-scale supersymmetry. We further
distinguish between models in which the gravitino mass is below and above the
inflationary scale. We examine the mass spectra of the inflationary sector. We
also consider in detail mechanisms for leptogenesis for each model when a
right-handed neutrino sector, used in the seesaw mechanism to generate neutrino
masses, is employed. In the case of C-models, reheating occurs via inflaton
decay to two Higgs bosons. However, there is a direct decay channel to the
lightest right-handed neutrino which leads to non-thermal leptogenesis. In the
case of WZ-models, in order to achieve reheating, we associate the matter-like
inflaton with one of the right-handed sneutrinos whose decay to the lightest
right handed neutrino simultaneously reheats the Universe and generates the
baryon asymmetry through leptogenesis.
