An early epoch of inflationary expansion would explain the isotropy and flatness of the Universe and provide the seeds for the CMB anisotropies and large scale structure formation. Over the last decade, string theory has provided a well-motivated framework to address the microscopic nature of inflation and its sensitivity to quantum gravity effects. However the post-inflationary epoch has been relatively little explored so far. The main cosmological challenges to be addressed include pre- and re-heating, the origin of the matter-antimatter asymmetry, the nature of dark matter, dark radiation and dark energy. String theory -- with its unified description of gravity and particle physics -- provides a promising framework to address these conne...