The effect of moving slamming load represents a long-standing issue in the design of marine structures against slamming, which has not yet been fully accounted for. Extensive full-scale measurements and model tests indicate that the peak slamming pressure region can move rapidly along the structural surface, exhibiting distinct load migration characteristics. However, current structural design methods and classification society rules usually simplify slamming loads as a uniformly distributed pressure, without fully accounting for the effect of load migration on the structural dynamic response. Focusing on moving slamming loads of hull structures, this paper briefly reviews advances in relevant experimental observations, dynamic response analyses, and engineering design methods. First, the formation and engineering background of moving slamming loads are introduced. Typical research findings obtained from full-scale measurements, model tests, and hydroelastic tests are summarized, and the influence of load migration on the response characteristics of grillage structures is analyzed. Subsequently, the fundamental concept and derivation of equivalent design pressure are elaborated. The equivalent design pressure method for moving slamming loads based on the dynamic-static equivalence principle and its analytical models are highlighted. Finally, the applicability, key influencing factors, and engineering application prospects of this method are discussed. Studies show that considering the load migration effect is of great significance for reasonably evaluating the slamming response of hull structures and developing design methods that balance physical rationality and engineering practicality.