Abadi M., Galves A. Inequalities for the occurrence times of rare events in mixing processes. The state of the art. (38K, LATeX 2e) ABSTRACT. The first occurrence time of a rare event in a mixing process typically has a distribution which can be well approximated by the exponential law. In this paper we review recent theorems giving upper bounds for the error term of this approximation. We shall focus on papers treating the problem in a general mixing framework.