Identification and detection of toxic/explosive environmental gases are of paramount importance to various sectors such as oil/gas industries, defense, industrial processing, and civilian security. Surface acoustic wave (SAW)-based gas sensors have recently gained significant attention, owing to their desirable sensitivity, fast response/recovery time, wireless capabilities, and reliability. For detecting various types of targeted gases, SAW sensors with different device structures and sensitive materials have been developed with diversified working mechanisms. This paper is focused on overviewing recent advances in working mechanisms and theories of dominant sensitive materials and key mechanisms/principles for targeting various gases in the realm of SAW gas sensors. The basic sensing theories and parameters of SAW gas sensors are briefly discussed, and then the major influencing factors are systematically reviewed, including the effects of various sensitive layer materials, temperature/humidity, and UV illumination on the overall performance of SAW gas sensors. We further highlight the relationships and adsorption/desorption principles between sensing materials and key targeted gases, including NH3, NO2, H2S, explosive gases of H2, and 2,4,6-trinitrotoluene, and organic gases of isopropanol, ethanol, and acetone, as well as others gases of CO, SO2, and HCl. Finally, we discuss key challenges and future outlooks in designing methodologies of sensing materials and enhancing the performance of SAW gas sensors, offering fundamental guidance for developing SAW gas sensors with good sensing performance.