After an introduction on the construction of inflationary models in string theory, I will focus on cosmological implications of Dirac-Born-Infeld multi-field inflationary models. The non-canonical kinetic terms of the Dirac-Born-Infeld action suggest an interesting alternative to slow roll inflation, and an embedding in string theory provide natural motivations for considering multi-field models. I will first discuss the general properties of inflationary trajectories in this framework. Then, I will present the main features of the behavior of cosmological perturbations, emphasizing their distinctive properties in comparison to standard slow-roll inflation.