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This paper discusses important hybrid aspects of chemical processing plants. It is outlined that discrete phenomena occur both on the physical level and in the control of these plants. As the dynamics of the transformations of energy and material are predominantly continuous, large and complex hybrid systems arise. We focus on three different aspects of dealing with such systems: (1) Modeling and simulation of hybrid systems for the design and optimization of plants, controllers and operating strategies. We present powerful simulation environments that have been developed in recent years. (2) Validation of plant instrumentation and discrete controllers. These systems are largely responsible for the safe and economic operation of chemical plants and the protection of the workforce, and the environment. Techniques for the verification of discrete controllers for continuous processes are discussed, which are based on a discrete approximation of the continuous dynamics. (3) Scheduling of batch plants. For plants that are operated in a discontinuous fashion, the timing and sequencing of the operations are very important for the efficient use of the equipment. This leads to large mixed-integer optimization problems. For a typical example, we show how the process and the constraints can be modeled and describe an efficient solution algorithm.