Abstract: Biomimetic amphibious robots can efficiently perform tasks in different environments by imitating the structure, function and behavior of natural organisms, and demonstrate broad application prospects. This paper discusses the morphological design theory of biomimetic robots from four aspects, i.e., structural bionics, functional bionics, behavior bionics, and coupled bionics. The biomimetic amphibious robots can be divided into four types according to their working environments, such as the aquatic-terrestrial-aerial biomimetic amphibious robots, the aquatic-terrestrial biomimetic amphibious robots, the terrestrial-aerial biomimetic amphibious robots, and the aquatic-aerial biomimetic amphibious robots. The research status of these four types of robots at home and abroad is discussed from the perspectives of structural features, motion mechanisms, and functional realization. Several challenges hindering the development of biomimetic amphibious robots are identified, such as the insufficient acquisition of biological cases, the inadequate cross-disciplinary knowledge reasoning mechanisms, the lack of flexibility in system control methods, the generally low intelligence levels, and the inefficient energy utilization. Finally, the prospects for biomimetic amphibious robots are explored from scientific and engineering perspectives. The critical role of biological and material sciences in the development of biomimetic amphibious robots is highlighted. The paper suggests that biomimetic amphibious robots can be developed in conjunction with technologies such as large language models, swarm intelligence, and data-driven design, along with optimizing morphological design and actuation distribution, which will collectively advance their adaptability, autonomy, and intelligence.