The article discusses the increasing importance of green hydrogen as an alternative energy source for various industrial processes and mobility solutions. Thermochemical hydrogen compressors, utilizing interstitial AB2 hydrides and metal hydride (MH) applications, are highlighted for their potential in hydrogen storage and distribution. The thermodynamics of hydride formation enable efficient hydrogen compression through temperature cycling, driven by waste heat, offering a silent operation suitable for urban environments. The use of AB5 and AB2 alloys in different compression stages has been explored in prototypes and lab-scale compressors, showcasing their ability to achieve high pressure outputs. Additionally, hybrid compression systems have been developed, combining mechanical or electrochemical low-pressure stages with metal hydride-based high-pressure stages to enhance overall efficiency. The article emphasizes the significance of thermochemical compression in establishing a safe, environmentally friendly, and sustainable energy distribution system for the widespread adoption of green hydrogen.