We review results on hadron multiplicities in high energy particle
collisions. Both theory and experiment are discussed. The general procedures
used to describe particle multiplicity in Quantum Chromodynamics (QCD) are
summarized. The QCD equations for the generating functions of the multiplicity
distributions are presented both for fixed and running coupling strengths. The
mean multiplicities of gluon and quark jets, their ratio, higher moments, and
the slopes of multiplicities as a function of energy scale, are among the main
global features of multiplicity for which QCD results exist. Recent data from
high energy e+e- experiments, including results for separated quark and gluon
jets, allow rather direct tests of these results. The theoretical predictions
are generally quite successful when confronted with data. Jet and subjet
multiplicities are described. Multiplicity in limited regions of phase space is
discussed in the context of intermittency and fractality. The problem of
singularities in the generating functions is formulated. Some special features
of average multiplicities in heavy quark jets are described.Comment: 140 pages, 33 figures, version for Physics Report