The consensus stability problem of the stochastic multi-agent systems is summarized, which is classified into four classes: the consensus stability problem of stochastic multi-agent systems with noises, the consensus stability problem of stochastic multi-agent systems with switching topologies, the consensus stability problem of stochastic delay multi-agent systems and the consensus stability problem of stochastic multi-agent systems with distributed optimization. Therefore, the study process for the stability of stochastic multi-agent systems is clarified, in which the existing problems are stated. Finally, conclusions are addressed and some future problems are given.