One goal of string cosmology is to construct and study well motivated inflationary scenarios and look for distintive observational signatures. A particular scenario is brane inflation, which realizes inflation in a geometrical way as the motion of D-branes through space, and can connect cosmology and extra dimensions in interesting ways. I will discuss some recent work in which details of the geometry of warped throats in string theory affect important aspects of inflation such as the spectrum of primordial perturbations.