  Microlensing observations have now become a useful tool in searching for
non--luminous astrophysical compact objects (brown dwarfs, faint stars, neutron
stars, black holes and even planets). Originally conceived for establishing
whether the halo of the Galaxy is composed of this type of objects, the ongoing
searches are actually also sensitive to the dark constituents of other Galactic
components (thin and thick disks, outer spheroid, bulge). We discuss here the
present searches for microlensing of stars in the Magellanic Clouds and in the
Galactic bulge (EROS, MACHO, OGLE and DUO collaborations). We analyse the
information which can be obtained regarding the spatial distribution and motion
of the lensing objects as well as about their mass function and their overall
contribution to the mass of the Galaxy. We also discuss the additional signals,
such as the parallax due to the motion of the Earth, the effects due to the
finite source size and the lensing events involving binary objects, which can
further constrain the lens properties.
  We describe the future prospects for these searches and the further proposed
observations which could help to elucidate these issues, such as microlensing
of stars in the Andromeda galaxy, satellite parallax measurements and infrared
observations.
