Oscillations abound in biological systems. Examples range from cardiac and neural rhythms to a variety of cellular rhythms of nonelectrical nature, such as glycolytic oscillations in yeast, cyclic AMP oscillations and waves in Dictyostelium amoebae, Ca++ oscillations, the segmentation clock responsible for somite formation in embryonic development, circadian clocks driving the sleep-wake cycle in mammals, and the oscillator driving the cell cycle. The mathematical modeling of these oscillatory phenomena shows how biological rhythms display common properties despite marked differences in their period and molecular mechanism. Physiological disorders in the form of dynamical diseases are often associated with the malfunction of these rhythms. Multiple layers of regulation by feedback loops and the cooperativity of biological processes provide the sources of nonlinearity responsible for the onset of oscillatory behavior in biological systems.