Heart rate variability has been analyzed conventionally with time and frequency domain methods, which measure the overall magnitude of RR interval fluctuations around its mean value or the magnitude of fluctuations in some predetermined frequencies. Analysis of heart rate dynamics by methods based on chaos theory and nonlinear system theory has gained recent interest. This interest is based on observations suggesting that the mechanisms involved in cardiovascular regulation likely interact with each other in a nonlinear way. Furthermore, recent observational studies suggest that some indexes describing nonlinear heart rate dynamics, such as fractal scaling exponents, may provide more powerful prognostic information than the traditional heart rate variability indexes. In particular, the short-term fractal scaling exponent measured by the detrended fluctuation analysis method has predicted fatal cardiovascular events in various populations. Approximate entropy, a nonlinear index of heart rate dynamics, that describes the complexity of RR interval behavior, has provided information on the vulnerability to atrial fibrillation. Many other nonlinear indexes, e.g., Lyapunov exponent and correlation dimensions, also give information on the characteristics of heart rate dynamics, but their clinical utility is not well established. Although concepts of chaos theory, fractal mathematics, and complexity measures of heart rate behavior in relation to cardiovascular physiology or various cardiovascular events are still far away from clinical medicine, they are a fruitful area for future research to expand our knowledge concerning the behavior of cardiovascular oscillations in normal healthy conditions as well as in disease states.