Inflation provides a compelling explanation of the observed features of the universe on cosmological scales. Yet, given the vast number of models, it may not be clear what precisely these observations tell us about the epoch of inflation. In this colloquium, I will explain how we are bridging this gap, both with a better understanding of the theory and with new observational probes. I will first review the historical motivations for inflation. I will then discuss recent theoretical work which organizes the signatures of models according to basic properties, like the number of degrees of freedom. I will conclude by discussing how this information is encoded in CMB and large scale structure data.