Hybrid systems are characterized by the interaction between continuous-time dynamics (governed by differential or difference equations), and discrete dynamics and logic rules (described by temporal logic, finite state machines, etc.). Recent progress in the theory and practice of modeling and control design have caused an increasing interest in the study of hybrid systems, which is motivated not only by theoretical challenges but also by their ability to model, analyze and synthesize controllers in a large variety of application areas. This paper highlights some aspects encountered when modeling with hybrid systems through a short overview of some controllability and stabilizability results concerning linear switching systems. It was shown how classical techniques, such as geometrical control theory, Lie-algebraic techniques, convex analysis find their applicability in the study of the behavior of the hybrid systems.