Microlensing observations have now become a useful tool in searching f
or non-luminous astrophysical compact objects (brown dwarfs, faint sta
rs, neutron stars, black holes and even planets). Originally conceived
for establishing whether the halo of the Galaxy is composed of this t
ype of objects, the ongoing searches are actually also sensitive to th
e dark constituents of other Galactic components (thin and thick disks
, outer spheroid, bulge). We discuss here the present searches for mic
rolensing 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 o
f the lensing objects as well as about their mass function and their o
verall contribution to the mass of the Galaxy. We also discuss the add
itional signals, such as the parallax due to the motion of the Earth,
the effects due to the finite source size and the lensing events invol
ving binary objects, which can further constrain the lens properties.
We describe the future prospects for these searches and the further pr
oposed observations which could help to elucidate these issues, such a
s microlensing of stars in the Andromeda galaxy, satellite parallax me
asurements and infrared observations.