Add to ORKGHybrid dynamics in process control arise for various reasons. The main source is the interaction between computer-realized discrete control functions and the continuous physico-chemical processes in the plant. But also physical or operational constraints lead to discrete phenomena in otherwise continuous processes. The modeling, the analysis and the design of hybrid control systems pose new problems for which the conventional systems and control theory is not an appropriate tool. The paper identifies these challenges using illustrative case studies and gives a survey of recent approaches to a formal treatment of hybrid systems. Particular emphasis is put on methods which were developed in computer science in the last years. We will discuss ...