Observations indicate a phase change of the Universe from neutral back to ionized after the first billion years of cosmic time (z ∼ 6). Two great unknowns persist regarding this cosmic reionization: what caused it, and how? Using a sample of nearby (z ∼ 0.3) galaxies, I answer these questions. First, I undertake careful measurements of the emergent ionizing radiation and other properties of 89 galaxies. Then, I compare the escape of this ionizing radiation to those properties, finding small, faint galaxies with concentrated star formation are the most prodigious ionizing radiation emitters. To understand the role of star formation in the escape of ionizing radiation, I develop a new method for modeling galactic winds that connects feedback mechanisms and outflow properties with observations. Finally, I characterize the stellar populations, the interstellar material, and the interplay between them in galaxies leaking ionizing radiation. I find that bursty star formation optimizes feedback for ionizing radiation escape from galaxies. The application of my results to recent observations of high redshift galaxies provides the first empirical constraints on the progenitors of ionizing radiation in the early Universe. Bridging the gap between my low-redshift works and distant galaxies clears a path to understanding the origins of cosmic reionization.