  If compact baryonic objects contribute significantly to the dark matter in
our Galaxy, their mass function will present vital clues for galaxy formation
theories and star formation processes in the early Universe. Here we discuss
what one might expect to learn about the mass function of Galactic dark matter
from microlensing and from direct searches in the infrared and optical
wavebands. Current microlensing results from the \eros\/ collaboration already
constrain halo mass functions which extend below $10^{-4}~\sm$, whilst recent
\hst\/ observations place strong constraints on disc and halo dark matter mass
functions extending above $0.1~\sm$. Infrared observations should either detect
or constrain objects larger than $0.01~\sm$ in the near future. Objects below
$0.01~\sm$ should be detectable through microlensing, although the prospects of
determining their mass function depend critically on a number of factors.
