The operation of specialized robots in complex environments is fundamentally rooted in mechanical principles. Through the systematic characterization of bearing capacity, slippage, rheology, and other intrinsic mechanical behaviors of deformable terrain, a theoretical framework for robot-terrain interaction has been established, enabling bidirectional coupling between locomotion dynamics and terrain medium responses. Driven by progressive refinements in fundamental theories, advances in multiphase granular simulation tools, and the iterative development of multi-modal wheeled-legged locomotion mechanisms, specialized robots have evolved from motion planning under idealized laboratory conditions to achieving long-term, stable, and reliable operation in real-world extreme outdoor settings. Their adaptability to unstructured terrains, including mountainous wilderness, arid deserts, and extraterrestrial landscapes, is empowered by an embodied intelligence system grounded in core mechanical principles. Firstly, by reviewing typical cases of soil mechanics and granular medium mechanics in the areas of obstacle-crossing capability, anti-subsidence design, environmental adaptability, and practical applications in deep space field engineering for special robots, a comparative analysis was conducted among three types of robots: legged, wheeled, and bio-inspired special robots. Furthermore, the core bottlenecks that restricted the practical deployment of special robots in the wild and on extraterrestrial surfaces, as well as key objective conditions such as the time-varying mechanical properties of soil, wheel-foot ground sliding instability, and the lack of prior information on environmental mechanics were analyzed. Finally, the prospective research directions in this domain were outlined to guide future investigations.