Hydrogen storage technologies are key enablers for the development of low-emission, sustainable energy supply chains, primarily due to the versatility of hydrogen as a clean energy carrier. Hydrogen can be utilized in both stationary and mobile power applications, and as a low-environmental-impact energy source for various industrial sectors, provided it is produced from renewable resources. However, efficient hydrogen storage remains a significant technical challenge. Conventional storage methods, such as compressed and liquefied hydrogen, suffer from energy losses and limited gravimetric and volumetric energy densities, highlighting the need for innovative storage solutions. One promising approach is hydrogen storage in metal hydrides, which offers advantages such as high storage capacities and flexibility in the temperature and pressure conditions required for hydrogen uptake and release, depending on the chosen material. However, these systems necessitate the careful management of the heat generated and absorbed during hydrogen absorption and desorption processes. Thermal energy storage (TES) systems provide a means to enhance the energy efficiency and cost-effectiveness of metal hydride-based storage by effectively coupling thermal management with hydrogen storage processes. This review introduces metal hydride materials for hydrogen storage, focusing on their thermophysical, thermodynamic, and kinetic properties. Additionally, it explores TES materials, including sensible, latent, and thermochemical energy storage options, with emphasis on those that operate at temperatures compatible with widely studied hydride systems. A detailed analysis of notable metal hydride–TES coupled systems from the literature is provided. Finally, the review assesses potential future developments in the field, offering guidance for researchers and engineers in advancing innovative and efficient hydrogen energy systems.