This review article deals with hydro-pneumatic accumulators (HPAs) charged with nitrogen. The focus is on HPA models used in the study of the energy efficiency of hydraulic systems. Hydraulic circuits with HPA are presented along with their various applications for delivering the required volume of fluid, maintaining the required pressure, ensuring safe operation, safety stop, leak compensation, fluid volume change compensation, pulsation damping, and pressure shock absorption. A general regenerative hydraulic system and a general hybrid hydraulic system are also presented. The review focuses primarily on HPA computational, dynamic, and simulation models. Basic HPA calculation parameters and computational models of energy storage and thermodynamic cycle are presented. Various computational and dynamic models of HPA have been defined, such as the thermodynamic model, simulation model, dynamic model, pulsation damper model, and shock pulse damper model. Research projects that have used HPA in industrial hydraulic systems are reviewed, such as those maintaining operating pressure in an industrial 80 MN open-die hydraulic forging press and acting as a shock pulse absorber in the lifting and levelling module of a tracked mobile robotic bricklaying system. The development of energy storage technology in HPA from various sources is now a global challenge.