The distinguishing characteristic of hybrid systems is the interaction between a continuous-time and a discrete-event component. By modeling these different components using differential equations and finite state automata, it is possible to represent a wide range of phenomena present in physical and technological systems. This paper illustrates hybrid dynamics by several simple examples. Some of these examples illustrate properties of hybrid systems not present in purely continuous or purely discrete systems, while others illustrate application domains such as vehicle control and real-time systems. A mathematical model called a hybrid automaton is then introduced, to show how hybrid dynamics can be formally analyzed.