Foundations of standard microlensing theory are discussesd as applied
to stars in the Galactic bulge, Magellanic Clouds or other nearby gala
xies and gravitational microlenses assumed to lie in-between these sta
rs and the terrestrial observer. In contrast to the review article by
Gurevich et al. [48], microlensing by compact objects is mainly consid
ered. Criteria for the identification of microlensing events are discu
ssed as also are microlensing events not satisfying these criteria, su
ch as non-symmetrical light curves and chromatic and polarization effe
cts. Large Magellanic Cloud (LMC) and Galactic bulge microlensing data
of the MACHO group are discussed in detail and also LMC data of EROS
and Galactic bulge data of OGLE are presented. A detailed comparison o
f theoretical predictions and observations is given.