  A short review of the development of the Nambu-Jona-Lasinio (NJL) model is
given. The SU(2)x SU(2) and U(3)x U(3) local quark NJL models are considered.
The mechanisms of spontaneous breaking of chiral symmetry and vector dominance
are shown. The local NJL model allows us to describe the mass spectrum and main
strong and electroweak decays of the four ground-state nonets of pseudoscalar,
scalar, vector and axial-vector mesons. Applications of this model to the
description of mesons in hot and dense medium are discussed. It is shown that
for solving problems connected with the description of the meson radial
excitations and quark confinement it is necessary to consider a nonlocal
extension of the NJL model. The main attention is attracted to the description
of the methods used in different versions of the NJL model. Physical results
for low-energy hadron physics obtained in these models can be found in the
cited works.
