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In 1967, Faddeev and Popov were able to quantize the Yang-Mills theory byintroducing new particles called ghost through the introduction of a gauge.Ever since, this quantization has become a standard textbook item. Some yearslater, Gribov discovered that the gauge fixing was not complete, gauge copiescalled Gribov copies were still present and could affect the infrared region ofquantities like the gauge dependent gluon and ghost propagator. This featurewas often in literature related to confinement. Some years later, thesemi-classical approach of Gribov was generalized to all orders and theso-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 thesubsequent construction of the GZ action, including many other toipics relatedto the Gribov region. It is shown how the GZ action can be viewed as anon-perturbative tool which has relations with other approaches towardsconfinement. Many different features related to the GZ action shall bediscussed in detail, such as BRST breaking, the KO criterion, the propagators,etc. We shall also compare with the lattice data and other non-perturbativeapproaches, including stochastic quantization.

The Gribov problem and QCD dynamics