  In 1967, Faddeev and Popov were able to quantize the Yang-Mills theory by
introducing new particles called ghost through the introduction of a gauge.
Ever since, this quantization has become a standard textbook item. Some years
later, Gribov discovered that the gauge fixing was not complete, gauge copies
called Gribov copies were still present and could affect the infrared region of
quantities like the gauge dependent gluon and ghost propagator. This feature
was often in literature related to confinement. Some years later, the
semi-classical approach of Gribov was generalized to all orders and the
so-called GZ action was born. Ever since, many related articles were published.
This review tends to give a pedagogic review of the ideas of Gribov and the
subsequent construction of the GZ action, including many other toipics related
to the Gribov region. It is shown how the GZ action can be viewed as a
non-perturbative tool which has relations with other approaches towards
confinement. Many different features related to the GZ action shall be
discussed in detail, such as BRST breaking, the KO criterion, the propagators,
etc. We shall also compare with the lattice data and other non-perturbative
approaches, including stochastic quantization.
