The Faintest Dwarf Galaxies
  The lowest luminosity (L < 10^5 L_sun) Milky Way satellite galaxies represent
the extreme lower limit of the galaxy luminosity function. These ultra-faint
dwarfs are the oldest, most dark matter-dominated, most metal-poor, and least
chemically evolved stellar systems known. They therefore provide unique windows
into the formation of the first galaxies and the behavior of dark matter on
small scales. In this review, we summarize the discovery of ultra-faint dwarfs
in the Sloan Digital Sky Survey in 2005, and the subsequent observational and
theoretical progress in understanding their nature and origin. We describe
their stellar kinematics, chemical abundance patterns, structural properties,
stellar populations, orbits, and luminosity function, and what can be learned
from each type of measurement. We conclude that: (1) in most cases, the stellar
velocity dispersions of ultra-faint dwarfs are robust against systematic
uncertainties such as binary stars and foreground contamination; (2) the
chemical abundance patterns of stars in ultra-faint dwarfs require two sources
of r-process elements, one of which can likely be attributed to neutron star
mergers; (3) even under conservative assumptions, only a small fraction of
ultra-faint dwarfs may have suffered significant tidal stripping of their
stellar components; (4) determining the properties of the faintest dwarfs out
to the virial radius of the Milky Way will require very large investments of
observing time with future telescopes. Finally, we offer a look forward at the
observations that will be possible with future facilities as the push toward a
complete census of the Local Group dwarf galaxy population continues.
