The frog-inspired robots with amphibious locomotion ability have greatest application prospects and practical value in the fields of resource exploration and environmental reconnaissance. Although frog-inspired robots have been of interest over many years, research on frog-inspired amphibious robots is still in its infancy. Since the locomotion mechanism is the basis for the research of frog-inspired amphibious robots, the research methods of the single motion mechanism of frogs are firstly inductive analyzed, and a reference scheme is proposed to inspire the research on the amphibious motion mechanism. Then, we collect and introduce a systematic discussion of the research status of frog-inspired robots according to the locomotion mode. The characteristics of the robots are analyzed from the aspects of design concept, structural characteristics, driving method, and motion performance. Finally, the technical challenges faced by the research on the frog-inspired robots are analyzed, and the development trend is predicted. The authors hope that this study can provide an informative reference for future research in the direction of frog-inspired amphibious robot.