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Hierarchical state machines are finite state machines whose states themselves can be other state machines. Hierarchy is a useful construct in many modeling formalisms and tools for software design, requirements and testing. We summarize recent work on hierarchical state machines with or without concurrency. We discuss issues of expressiveness and succinctness, the complexity of basic operations (such as emptiness, equivalence etc.), and algorithmic problems in the analysis of hierarchical machines to check for their properties.