A critical overview of the method of characteristics (MOC) and its application to nuclear engineering problems is provided. After examining the mathematical basis of the method, its application to both single- and two-phase flow transients is described. Application of the MOC to neutronics calculations is also considered. Since most current interest in the MOC centers about its application to two-phase systems, this application area is emphasized. Of particular importance is the use of the method for analysis of well posedness of the basic governing equations. An important, but often overlooked, ability of the method is the provision of analytical solutions for transients where only two conservation equations need to be considered. These applications, as well as all of the other major applications of the MOC, are described.