Our Milky Way galaxy is surrounded by a flock of tiny satellite galaxies. These ultra-faint "dwarf" galaxies are the most ancient, most chemically pristine, and most dark-matter-dominated stellar systems known. Observations of these extreme galaxies provide a unique opportunity to better understand galaxy formation, the particle nature of dark matter, and the standard cold dark matter model of cosmology. Due to their low luminosity, the discovery of the faintest galaxies has only recently become possible thanks to the unprecedented sensitivity of digital sky surveys.  However, even with the most powerful telescopes, our census of the faintest galaxies is still far from complete. I will describe recent advances in the search for our smallest galactic neighbors and how these observations can help answer some of the biggest questions in cosmology.