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Importance factors are indicators of the risk significance of the components of a system. They are widely used in probabilistic safety analyses to rank components according to their contribution to the global risk. In this article, we review definitions and interpretations of importance factors in the case the support model is a coherent fault tree, and failures of components are described by basic events of that fault tree. First, we show that each importance factor characterizes the probability of a certain set of minterms. The notion of critical states, that is, minterms in which failing/repairing the component suffices to fail/repair the system, plays a central role in this process. Then, we discuss assessment algorithms for the two main technologies at hand: minimal cutsets and binary decision diagrams. Finally, we draw some practical conclusions from these developments. This article thus contributes to clarify mathematical and algorithmic foundations of importance factors.