Inflationary cosmology -- exponential expansion of the universe at early times -- provides a simple, observationally tested scenario for understanding the observed flatness and homogeneity of the universe and the seeds of structure formation. Within this broad framework, there are diverse mechanisms for inflation and the density perturbations, many of which make distinctive predictions for CMB observations. The mechanism behind inflation is sensitive to very high-energy physics, and requires input from an ultraviolet-complete theory of gravity (such as string theory). I will describe two particular observables of interest: a gravity wave signature from inflation, and non-Gaussian corrections to the power spectrum. Building on our progress stabilizing string compactifications in recent years, I will describe two basic mechanisms for inflation, each of which yields one of these distinctive signatures. Falsifiable on the basis of current and near-term planned CMB experiments which I will review, these examples are illustrative of the growing opportunities for trying to connect string theory with observations.