Over the past decade, classical mechanics has been transformed from an historical relic into a contemporary model for certain problems in atomic and molecular physics. This transformation has been brought about by recent interest in the study of chaotic dynamics in nonlinear classical systems. A good example is the behavior of highly excited atoms in microwave fields. In the language of classical mechanics a hydrogen atom in a microwave field is a periodically perturbed nonlinear oscillator. Depending on the strength of the perturbing microwave field, the equations of motion can become chaotic. The chaotic electron dynamics results in rapid ionization above a threshold microwave field strength. This paper presents the basic components of the classical models that we have introduced to describe this chaotic ionization of highly excited hydrogen atoms.