The distinctive characteristics of specific Phase Change Materials (PCMs) have garnered significant attention for their potential in Thermal Energy Storage (TES). However, the primary drawback of these materials lies in their low thermal conductivity. In contrast to active methods, a range of passive approaches have been proposed, developed, and systematically assessed to enhance PCM efficiency, each with its own set of advantages and disadvantages. One such passive technique involves incorporating thermally conductive nanoparticles to produce Nano-enhanced PCMs (NePCMs). Depending on the type of nanoparticles employed, NePCMs can possess magnetic, electrical conductivity, or both properties and can be influenced by Magnetic Fields (MFs). This study offers a comprehensive review of the active application of magnetic force to provide valuable insights into the current state of knowledge, key findings, and potential applications of NePCMs in magnetically assisted TES systems. It covers both numerical and experimental investigations, including the development of numerical models and solution techniques. Additionally, the review explores magnetic parameters such as the direction, strength, and gradient of MFs, along with the type of nanoparticles influencing magnetic effects. The findings reveal that MFs have the capability to finely control fluid dynamics and heat transfer, consequently enhancing energy storage efficiency. This influence significantly impacts the charge and discharge processes of NePCMs, leading to improved process times and alterations in both the shape of the solid-liquid interface and the mushy zone. This review also elucidates the current challenges in the application of MFs on NePCMs and discusses potential strategies to tackle these challenges.