Abstract: The combined sky coverage and depth of modern wide-area ground-based optical imaging surveys, in particular the Dark Energy Survey, have made possible the discovery and cataloging of the least luminous known galaxies. The demographics of faint dwarf galaxies throughout our local environment and the properties of the smallest individual ultrafaint galaxies have broad implications for astrophysics. I have designed and implemented search algorithms to identify faint dwarf galaxies both within the gravitational influence of the Milky Way and beyond out to the edges of the Local Group. The census of ultrafaint Milky Way satellites has placed competitive constraints on several alternative dark matter models, established the importance of the Large Magellanic Cloud in the formation of our local galactic environment, and increased our understanding of the connection between the smallest galaxies and the dark matter halos that host them. The search for faint field dwarf galaxies beyond the Milky Way uncovered one of the most diffuse dwarf galaxies ever discovered, the largest galaxy known at its luminosity. By comparing the current catalog of nearby dwarf galaxies to the results of searches over simulated versions of the Local Group, I conclude that we have likely exhausted the power of searches for resolved stellar populations in current wide-area sky coverage. Looking forward, this work informs what we might expect to discover in future surveys covering new areas of sky or with deeper data and how these discoveries will change our understanding of the particle properties of dark matter and the nature of galaxy formation.