There are critical outstanding questions about the formation of galaxies, and their impact on the intergalactic medium (IGM). One important goal is to determine the origin of the ultraviolet radiation field that reionized the universe and maintained the ionization of the IGM. This question becomes more pressing as we discover ever more distant galaxies, probing back to the earliest epochs and approaching the formation of the first stars. Simultaneously, we are preparing for novel radio telescopes to come on-line and probe the global phase transition of gas in the early universe. I will review the latest observational results about the escape of ionizing radiation from star-forming galaxies in the early universe, and highlight several promising new directions forward.