Hybrid systems in their broad sense represent an extremely large class of systems. From the technical and technological points of view, systems that contain analog and digital components, systems that comprise parts of different physical natures such as biological, chemical, electrical, electronic, hydraulic, mechanical, and/or pneumatic ones, are hybrid systems. From the mathematical standpoint, systems with the parts described by mathematical models of different forms, such as algebraic equations, difference equations, ordinary differential equations, and/or partial differential equations, are hybrid systems. From the signal transmission viewpoint, systems through some parts of which signals propagate continuously in time, and through other parts of which signals are transmitted and processed only in discrete moments and/or only during very short time intervals are also hybrid systems, which form the hybrid systems in the close sense. All these combinations exist and characterize many control systems, which are in reality nonlinear. Engineers have designed and constructed them for a long time. However, the related unified and effective theory, that would enable their further advancements, has not so far existed. One of the main reasons is their extreme complexity and the inadequacy of the mathematical tools to model and treat them. In this regard, the Editor takes the freedom to point out the following Principle that is important for applicability and for the exact realizability of the theoretical results on control synthesis. The Time Continuous and Uniqueness Principle discovered recently expresses the fact that the value of every physical variable changes only continuously in time by passing through every intermediate value between its initial and final value, and by possessing a unique value in one place at any moment. Consequently, adequate mathematical models should describe and express this time continuity. Any synthesized control should be uniquely defined and continuous in time. This leads to completely continuous-time models of hybrid systems with time-varying parameters and nonlinearities, if all their variables are physical variables. The current trend is, by ignoring fast transients, to allow discontinuities as instantaneous abrupt changes of values of physical variables, which essentially violates the Principle. In spite of such inherent qualitative simplification, the mathematical models obtained are still very complex. The papers of this special issue reflect this complexity and contribute with diverse approaches to coping with their complexity.