Supersymmetric string theories are the best candidates we have for a unification of all the fundamental interactions known in physics. These theories still need to be confronted with experiment. However, direct evidence for string effects only becomes important at high energies. This means that, at present, one can only hope to constrain these theories through their low energy limits. Of these, the most promising are supergravities where the fields and their interactions are severely constrained by the superstring theory. In this thesis we will consider some of the additional constraints imposed by cosmology on these models. In the first part our attention will be focused on the problem of stabilising the dilaton field. The vacuum expectation value (vev) of the dilaton is related to both gauge and gravitational coupling constants. This means that for the theory to be realistic the dilaton needs to acquire a finite vev. The most popular way of doing this is through the condensation of gauginos. In this thesis we will propose a particular model where the dilaton is stabilised at reasonable values with a vanishing cosmological constant. We will also show a way of dynamically evolving the dilaton to this stable point in a cosmological setting. In a second part we will address the "moduli problem". Moduli fields arise generically in string-inspired theories, their vev being related to the compactification radius. The expected mass and coupling of these fields would make them incompatible with the standard nucleosynthesis scenario. Thermal inflation has been proposed as a mechanism that would permit one to solve this problem. In this thesis we will examine in detail how this mechanism can be implemented in a supergravity model and we will also consider the possibility of defect production in this scenario.