Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. This Ph.D. thesis studies various approaches to extend the RCM to the nonlinear domain. Nonlinearity has been introduced to study the statistics of generated harmonics and amplitude dependent responses of complex electromagnetic structures. The sources of nonlinearity that have been studied include circuit elements such as diodes, nonlinear dielectrics, and superconducting materials. Nonlinear systems in different scenarios are studied and the RCM is applied and extended to explain the statistical results. This is an important step in the ongoing effort to create the science of nonlinear wave chaos.