Because faint, low mass galaxies are numerous at high redshifts, their impact on the Universe is expected to be significant. They may host a substantial fraction of the Universe's star formation, provide many of the energetic photons needed to reionize the hydrogen gas surrounding galaxies, and affect their surroundings via powerful, starburst-driven galactic outflows. Because of their faintness, however, the properties of these galaxies are difficult to determine. I will discuss a variety of observations aimed at characterizing the physical conditions in low mass, low metallicity galaxies during the peak epoch of star formation, when the Universe was ~20% of its current age, with particular emphasis on the study of galactic outflows in faint galaxies.