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Classical reliability models consider the failure modes of a multicomponent system as independent phenomena, even if these modes concern only one component or neighbouring components. In fact, when a failure mode occurs on a given system, causes may be related to external events or to the physical degradation of any component in the system. In both cases, failure modes can partially or totally share some root causes, which may compromise the principle of independence of failure modes. This paper reviews the failure interaction models that characterise the effect of any failure mode of a component on the failure modes of its neighbors and on the entire system. Three relevant groups of interaction models are reviewed: reliability indexes' interaction, state-based interaction and copula-based interaction. All these models share the hypothesis of stochastic dependence between failure modes, also referred to as failure interaction. They differ in their fundamental modeling concepts. Advantages and limits of each of them are emphasized in a comparative study dealing with dependency concepts, modeling methods and application domains.