The observed properties of the primordial fluctuations can provide constraints on physical theories in regimes otherwise inaccessible to experiment. A cornucopia of precision cosmological data combined with theoretical advances have recently resulted in dramatic progress in understanding the physics of the early universe. I will present two vignettes of my recent work in this area. (1) The shape of the primordial power spectrum is one of the most useful cosmological observables. I will present a powerful technique for reconstructing this shape, and discuss its application to cosmological data from the cosmic microwave background (CMB), galaxy surveys and the Lyman alpha forest flux power spectrum. (2) Theories aiming to provide a "complete" description of cosmic history predict that our observable universe resides inside a single bubble embedded in a vast inflating multiverse. Collisions between bubble universes imprinted in the CMB sky provide a powerful observational test of this idea. I will describe a robust algorithm for non-Gaussian source detection in massive datasets, and present its application to the search for bubble collision signatures in CMB data.