What is a Galaxy?

Over the last decade, Galactic science has been revolutionized by the maps made possible by the Sloan Digital Sky Survey.  These maps revealed the large scale structure and substructure of the Milky Way's primary components and revealed a new population of ultra-faint dwarf galaxies orbiting the Milky Way.  These dwarfs are 100 times less luminous than any galaxy previously known, a million times less luminous than the Milky Way itself, and may be the most numerous type of galaxy in the universe.  The Milky Way's ultra-faint dwarf population is currently our best tracer of dark matter on subgalactic scales, making a well-defined census and careful studies of these objects essential tests for cold dark matter models on such scales. This talk will highlight recent observational progress in and current obstacles to our understanding of dark matter and galaxy formation at the smallest scales, including: i. the results of recent photometric and spectroscopic observations of the Milky Way's least luminous and most distant companions, placing them in cosmological context, ii. the challenges facing efforts to measure the presence of dark matter in low luminosity and/or compact stellar systems, and iii. the status of an ongoing search for nearby dwarf galaxies in RCS2/CFHTLS survey data.