Understanding cosmic reionization requires the identification and characterization of early sources of hydrogen-ionizing photons. The 2012 Hubble Ultra Deep Field (UDF12) campaign acquired the deepest blank-field infrared images with the Wide Field Camera 3 aboard Hubble Space Telescope and, for the first time, systematically explored the galaxy population deep into the era when cosmic microwave background (CMB) data indicate reionization was underway. High-redshift observations with HST including UDF12, CANDELS, and the Frontier Fields provide the best constraints to date on the abundance, luminosity distribution, and spectral properties of early star-forming galaxies. We synthesize results from these HST campaigns and the most recent constraints from Planck CMB observations to infer redshift-dependent ultraviolet luminosity densities, reionization histories, and the electron scattering optical depth evolution consistent with the available data. We review these results, and discuss future avenues for progress in understanding the epoch of reionization.