This review is devoted to the Statistical Multifragmentation Model (SM
FM) developed in Copenhagen more than 10 years ago and widely used now
for interpreting experimental data on multiple fragment production in
different nuclear reactions. The model is based on the assumption of
simultaneous break-up of a thermalized nuclear system. Basic principle
s and different realizations of the statistical approach to the nuclea
r multifragmentation are described in detail. Special emphasis is put
on the implementation of specific nuclear features such as finite size
effects, internal excitation of fragments, their strong and Coulomb i
nteraction. Hot primary fragments are treated within the liquid-drop a
pproximation. An efficient Monte Carlo method is proposed for generati
ng microcanonical ensembles of break-up channels. Deexcitation of hot
fragments via evaporation and Fermi break-up is also included in the n
umerical code. The evolution of nuclear disintegration mechanisms with
increasing excitation energy, from compound nucleus to multifragmenta
tion and vaporization, follows naturally from the model. Observable si
gnals of multifragmentation are discussed and numerous applications of
the model for analyzing experimental data are demonstrated. In partic
ular, hybrid models, combining dynamical simulations of non-equilibriu
m stages of the reaction with statistical break-up of thermalized inte
rmediate systems, are described. The ''backtracing'' method of reconst
ructing parameters of decaying sources from experimental data is also
presented.