The LCDM cosmological model accounts for an impressive array of data on
the large-scale structure of the universe, from scales of a few
megaparsecs to a few gigaparsecs. On submegaparsec scales, however, the
model cannot be tested with the same degree of rigour as on larger scales
where microwave background radiation data and measures of galaxy
clustering provide clean and well-understood diagnostics. Yet, it is
precisely on these small scales that the nature of the dark matter
manifests itself most clearly. I will discuss theoretical predictions for
the small-scale structure of the universe which appear to be discrepant
with recent kinematical data for satellite galaxies of the Milky Way.
Possible solutions range from the relatively mundane - that the mass of
our galaxy is smaller than is often thought - through exotic baryonic
processes to the more radical assumption that the dark matter is not what
the standard theory assumes.