A variety of mathematical methods have been developed to characterize complex rhythms that are observed in physiological systems. These methods include classical techniques such as the mean, standard deviation, and power spectrum, as well as newer methods suggested by nonlinear dynamics including the dimension, Lyapunov number, and entropy. This paper reviews the various ways in which these measures have been applied to analyze physiological dynamics with emphasis on the potential advantages and pitfalls of the various approaches. We conclude that these methods may be useful to help characterize complex time series, but only rarely is it possible to use these methods to establish deterministic chaos in a given time series.