The goal of much effort in recent years has been to provide a simplified interpretation of the electroencephalogram (EEG) for a variety of applications, including the diagnosis of neurological disorders and the intraoperative monitoring of anesthetic efficacy and cerebral ischemia. Although processed EEG variables have enjoyed limited success for specific applications, few acceptable standards have emerged. In part, this may be attributed to the fact that commonly used signal processing tools do not quantify all of the information available in the EEG. Power spectral analysis, for example, quantifies only power distribution as a function of frequency, ignoring phase information. It also makes the assumption that the signal arises from a linear process, thereby ignoring potential interaction between components of the signal that are manifested as phase coupling, a common phenomenon in signals generated from nonlinear sources such as the central nervous system (CNS). This tutorial describes bispectral analysis, a method of signal processing that quantifies the degree of phase coupling between the components of a signal such as the EEG. The basic theory underlying bispectral analysis is explained in detail, and information obtained from bispectral analysis is compared with that available from the power spectrum. The concept of a bispectral index is introduced. Finally, several model signals, as well as a representative clinical case, are analyzed using bispectral analysis, and the results are interpreted.