Screw-driven robots have found extensive applications in operations across soft and wet terrains such as river and beach mudflats, swamps, wetlands, and snowfields, due to their merits of low ground pressure, high thrust capacity, and superior mobility. The developmental trajectory of screw-driven robots was first traced from the 18th century onward, then their locomotion principles were analyzed. It proceeds to systematically summarize and elaborate on the current state of domestic and international research, with a focus on key aspects: the screw propulsion mechanism and its actuation system, optimization of structural parameters for screw-based propulsion, the interaction mechanism between the locomotion system and environmental media, and modeling of the propulsion unit along with its motion control strategies. The development trends and research hotspots of the spiral-propulsion robot were discussed, namely, the study of more reasonable topological structures of multi-spiral propulsion mechanisms and their more optimal parameter combinations, further revealing the interaction mechanism between the spiral propulsion mechanism and the environmental medium, constructing more accurate dynamic models, and researching intelligent control algorithms for the spiral-propulsion robot, expanding its multi-scenario applications, with the aim of providing references for the research and application of spiral-propulsion robots.