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Surface acoustic wave (SAW) devices are one of the indispensable components in the radio frequency (RF) front-end of mobile phones. With the development of mobile communication technology, the requirements for linear specification of devices are more and more strict. Nonlinear distortions of SAW devices have a serious influence on the application of mobile RF modules. To satisfy the strict requirement of linearity of communication system, it is necessary to understand the generation mechanism of nonlinearity and study the accurate modeling, appropriate measurement methods, and nonlinear response elimination technology. In this paper, we summarize the research progress on the nonlinearity of SAW devices in recent years from four aspects: the generation mechanism, simulation methods, measurement system, and suppression technology. The nonlinear harmonics with the nonlinear Mason equivalent circuit model are simulated. Furthermore, harmonics and intermodulation signals of SAW filters are tested by the authors. Thanks to these research studies, it is of great significance to the development of future RF front-end modules with high linear SAW devices.