This chapter presents a brief comparison of ideal and real gas behavior, emphasizing how non-ideal effects significantly influence the work required for hydrogen compression at high pressures. It introduces a comprehensive methodology for calculating compression work using two complementary approaches: the direct method, which integrates pressure and volume relations, and the indirect method based on enthalpy changes. A detailed comparison of isentropic and isothermal compression is included, demonstrating that isothermal compression requires the least work input, whereas isentropic compression demands higher work due to temperature rise and increased enthalpy. The chapter also highlights the role of the isentropic exponent in defining process behavior and presents a modeling framework for hydrogen storage that incorporates real gas effects, multistage compression, and thermal evolution. Overall, the methodologies and analyses provided enable accurate work estimation and support the design of efficient hydrogen compression and storage systems.