Complex cross-media dynamic mechanisms are involved in the water obstacle crossing of amphibious vehicles, which is considered the critical bottleneck restricting their all-domain mobility. The research progress on the multi-physics coupled dynamic characteristics and control strategies of amphibious vehicles during the entire cycle of water entry, water navigation, and water egress is systematically reviewed to improve the design and optimization of their obstacle-crossing capabilities. For the water entry phase, the posture instability triggered by transient fluid slamming loads is highlighted, and it is demonstrated that these impacts can be effectively mitigated through bow configuration optimization, the application of flexible shock absorption technologies, and the implementation of active posture control. During the water navigation phase, to enhance cruising speed, the application boundaries, advantages, and disadvantages of passive appendage drag reduction, novel surface air-curtain/bionic drag reduction, and active posture adjustment technologies are comparatively analyzed. For the highly risky water egress phase, the difficulties of vehicle slipping and bogging down—induced by buoyancy attenuation and surging ground driving resistance—are clarified, and the construction of a computational fluid dynamics and multi-body dynamics (CFD-MBD) co-simulation framework is emphasized as an effective approach for predicting dynamic characteristics in the water-land transition zone. Finally, it is concluded that the exploration of cooperative control strategies based on the optimal slip ratio, dynamic torque allocation, and water propulsion systems is a crucial future development direction for enhancing the obstacle-crossing success rate and all-terrain adaptive capacity of amphibious equipment.