This paper studies the semantics of hierarchical finite state machines (FSM's) that are composed using various concurrency models, particularly dataflow, discrete-events, and synchronous/reactive modeling. It is argued that all three combinations are useful, and that the concurrency model can be selected independently of the decision to use hierarchical FSM's. In contrast, most formalisms that combine FSM's with concurrency models, such as statecharts (and its variants) and hybrid systems, tightly integrate the FSM semantics with the concurrency semantics. An implementation that supports three combinations is described.