In particular orbifold compactifications of string theory which are constrained by target-space duality symmetry offer as natural candidates for the role of inflatons the orbifold moduli. Orbifold moduli dynamics is very constrained by duality symmetry and offers a concrete framework for discussing Cosmological Inflation. We discuss the resulting cosmology assuming that non-perturbative dynamics generates a moduli potential which respects target-space modular invariance.

We also review scale-factor duality and Pre-Big-Bang scenarios in which inflation is driven by the kinetic terms of the dilaton modulus. In this context we discuss the problem of graceful exit and review recent attempts for solving the problem of exiting from inflation. The possibility of obtaining inflation through the D-terms in string models with anomalous U_A(1) and other Abelian factors is reviewed.
In this context we discuss how the slow-roll problem in supergravity models with F-term inflation can be solved by D-term inflation. We also briefly review the consequences of duality for a generalised Heisenberg uncertainty principle and the structure of space-time at short scales. The problem of the Cosmological Constant is also briefly discussed.