Hydrogen as a clean fuel is becoming vital in view of depleting fossil fuels and ever increasing energy demand. Hence hydrogen generation and storage gains immense importance. In this review article, different methods of hydrogen storage viz., physical, chemical and electrochemical in various forms like gas, liquid and solid have been discussed and compared in terms of their efficacy, capacity, operating conditions and other safety aspects. Modeling and simulation studies reported on various aspects of hydrogen storage have been presented and compared vis a vis governing equations, applications, assumptions, merits and demerits. These modeling studies would enable to understand the phenomenon better and to explore new avenues. Kinetic and thermodynamic aspects of hydrogen storage especially employing metal hydrides have been discussed too to understand the mechanism, rate controlling actors and energy aspects. Future challenges and prospects of all the aspects of the review were provided.