This article analyzes the processes of compressing hydrogen in the gaseous state, an aspect considered important due to its contribution to the greater diffusion of hydrogen in both the civil and industrial sectors. This article begins by providing a concise overview and comparison of diverse hydrogen-storage methodologies, laying the groundwork with an in-depth analysis of hydrogen’s thermophysical properties. It scrutinizes plausible configurations for hydrogen compression, aiming to strike a delicate balance between energy consumption, derived from the fuel itself, and the requisite number of compression stages. Notably, to render hydrogen storage competitive in terms of volume, pressures of at least 350 bar are deemed essential, albeit at an energy cost amounting to approximately 10% of the fuel’s calorific value. Multi-stage compression emerges as a crucial strategy, not solely for energy efficiency, but also to curtail temperature rises, with an upper limit set at 200 °C. This nuanced approach is underlined by the exploration of compression levels commonly cited in the literature, particularly 350 bar and 700 bar. The study advocates for a three-stage compression system as a pragmatic compromise, capable of achieving high-pressure solutions while keeping compression work below 10 MJ/kg, a threshold indicative of sustainable energy utilization.