The classical dynamics of the inflationary era explains the large-scale homogeneity, isotropy and flatness of the universe, while microscopic quantum fluctuations during inflation account for the primordial inhomogeneities observed in the cosmic microwave background. However, while inflation is fantastically successful as a phenomenological model of the early universe, a detailed understanding of the physical origin of the inflationary expansion has remained elusive. In this talk I will review recent advances in the ambitious pursuit to derive the physics of inflation from string theory. I will describe what I believe to be the primary theme of the subject: the sensitivity of inflation to Planck-scale physics. Concretely, I will highlight two specific aspects of inflation (the flatness of the potential and the amplitude of gravitational waves) that depend sensitively on the ultraviolet (UV) structure of the theory. To illustrate these general remarks, I will give two case studies: `warped D-brane inflation' and `axion monodromy inflation'.
The talk is based on an upcoming review article with Liam McAllister. I will try to present the material in a way that is accessible to both astrophysicists and high energy theorists.