The evolution of massive stars in close binary systems is significantly
different from single star evolution due to a series of interactions between
the two stellar components. Such massive close binary systems are linked
to various astrophysical phenomena, for example Wolf-Rayet stars, supernova
type Ib and Ic, X-ray binaries and gamma-ray bursts. Also, the emission of
gravitational waves, recently observed by the LIGO-Virgo detectors, is
associated with mergers in binary systems containing compact objects, relics
of massive stars - black holes and neutron stars. Evolutionary calculations of massive close binary systems were performed by various authors,
but many aspects are not yet fully understood. In this paper, the main
concepts of massive close binary evolution are reviewed, together with the
most important parameters that can influence the final outcome of the binary
system evolution, such as rotation, magnetic fields, stellar wind mass loss
and mass accretion efficiency during interactions. An extensive literature
overview of massive close binary models in the light of exciting
observations connected with those systems is presented.