Four dimensional effective actions of many of the currently studied extra-dimensional theories seem to contain massless scalar fields called moduli. Giving these fields a potential is crucial to make these theories compatible with observations. It is therefore natural to explore the possibility that before they settle down to the true minimum of their potentials these fields could be relevant for cosmology, in particular they could be the source of an inflationary expansion period of the universe. In this talk, I will review ealier attempts to follow these ideas and present a new model of topological modular inflation in the context of the recently develop flux compactifications within string theory.