We explore leptogenesis induced by the propagation of neutrinos in non-trivial gravitational backgrounds that may characterise the Early Universe epochs of various theories, including string theory. The key point in all these models is that the background induces different populations of fermions as compared to antifermions, and hence CPT Violation (CPTV), already in thermal equilibrium. Depending on the model, then, such populations may freeze out at various conditions leading to leptogenesis and baryogenesis. Among the considered scenarios, is a stringy one, in which the CPTV is associated with a cosmological background with torsion provided by the Kalb-Ramond antisymmetric tensor field (axion) of the string gravitational multiplet. We also discuss CPTV models that go beyond the local effective lagrangian framework, such as a stochastic (Lorentz Violating) Finsler metric and D-particle foam, where the CPTV is due to populations of stochastically fluctuating point-like space-time defects that can be encountered in string/brane theory (D0 branes).