Some important aspects of the behavior and control of physical systems can be studied using discrete event system models. One such model developed by Ramadge and Wonham is presented here with extensions to allow for partial observations and uncertainty in the state transitions. Although most of the paper is concerned with mathematical analysis, in particular the problem of controller synthesis, some remarks are devoted to clarify the important issues concerning the relations between the model and the real system. Finally, some suggestions are made concerning fruitful directions for further research.