Abstract: In polar ice-covered regions, the restoring force for wave motion at the ice-water interface includes not only gravity but also the elastic force of the ice layer. Such waves are known as hydroelastic waves (or flexural-gravity waves). Unlike ocean surface waves, the propagation characteristics of hydroelastic waves are governed not only by hydrodynamics but also significantly depend on the elastic properties of the ice layer. Its critical resonance regime differs entirely from that of pure gravity waves, exhibiting unique nonlinear wave phenomena near the critical velocity. This paper systematically reviews research progress on hydroelastic waves excited by moving loads, covering theoretical studies, numerical simulations, and experimental observations. Key focus areas include potential flow models, viscoelastic effects, nonlinear dynamics, and ice sheet responses under complex loading scenarios (e.g., accelerated motion, 3D effects, channel boundaries, and submerged loads). This paper provides critical theoretical and technical insights for polar resource exploitation, ship navigation safety, and the design of large-scale floating marine structures.