Motivated by phenomenological applications we consider (warped) compactifications of type IIA string theory on Calabi-Yau four-folds in the presence of Ramond-Ramond fluxes. The main goal of the talk is a description of low-energy physics, including new superspace formulation of two-dimensional N=(2,2) dilaton supergravity coupled to matter, and computation of the effective superpotentials induced by fluxes