Rapid advances in thermal management technology and the increasing need for multi-energy conversion have placed stringent energy efficiency requirements on next-generation shape-stable composite phase change materials (PCMs). Magnetically-responsive phase change thermal storage materials are considered an emerging concept for energy storage systems, enabling PCMs to perform unprecedented functions (such as green energy utilization, magnetic thermotherapy, drug release, etc.). The combination of multifunctional magnetic nanomaterials and PCMs is a milestone in the creation of advanced multifunctional composite PCMs. However, a timely and comprehensive review of composite PCMs based on magnetic nanoparticle modification is still missing. Herein, we furnish an exhaustive exposition elucidating the cutting-edge advancements in magnetically responsive composite PCMs. We delve deeply into the multifarious roles assumed by distinct nanoparticles within composite PCMs of varying dimensions, meticulously scrutinizing the intricate interplay between their architectures and thermophysical attributes. Moreover, we prognosticate future research trajectories, delineate alternative stratagems, and illuminate prospective avenues. This review is intended to stimulate broader academic interest in interdisciplinary fields and provide valuable insights into the development of next-generation magnetically-responsive composite PCMs.