We consider ammachine stochastic flow-shop and a set of n jobs, with known release dates, to be processed. In this paper, we distinguish two types of random events: processing times (job processing times are random variables which follow a probability distribution function) and breakdowns (time between failure and repair time are random variables). The main purpose of this paper is to review and to propose a classification for some developments about the static stochastic flow-shop scheduling problem. We propose also an extension of the notation of Graham, Lawler, Lenstra, and Rinnooy Kan in order to take into account random events.