Many nonlinear effects have been discovered and developed in photoacoustic imaging. These nonlinear mechanisms have been explored for different utilizations, such as enhancing imaging contrast, measuring tissue temperature, achieving super-resolution imaging, enabling functional imaging, and extracting important physical parameters. This review aims to introduce different nonlinear mechanisms in photoacoustics, underline the fundamental principles, highlight their representative applications, and outline the occurrence conditions and applicable range of each nonlinear mechanism. Furthermore, this review thoroughly discusses the nonlinearity rule concerning how the mathematical structure of the nonlinear dependence is correlated to its practical applications. This summarization is useful for identifying and guiding the potential applications of nonlinearity based on their mathematical expressions, and is helpful for new nonlinear mechanism discovery or implementation in the future, which facilitates further breakthroughs in nonlinear photoacoustics.