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Graphene has been employed in the methodological energy maneuvers due to remarkable structure and features, however the use is limited due to nanosheet aggregation issues. Metal-organic framework has also been used for energy systems, nevertheless possess low conductivity and stability issues towards application. This state-of-the-art review is designed to present essential aspects of graphene and metal-organic framework (MOF) hybrids and utilization towards the modern energy devices and systems. Amid energy storage devices, graphene-MOF hybrids have been found functional for lithium ion batteries, supercapacitors, and fuel cells. Graphene-MOF hybrids have been searched for surface area, structural, microstructural, and physical features. For the formation of hybrids related to energy systems, techniques such as template, heating, solution, in situ, hydrothermal, freeze-drying, chemical vapor deposition, and related facile methods have been used. Consequently, the electron conduction, electrochemical features, charge/energy density, charge-discharge, reversible capacity, cyclic stability, specific capacitance, electrocatalytic activity, oxygen reduction reactions, and other factors related to lithium ion batteries, supercapacitors, and fuel cells have been reported. For these systems, graphene-MOF hybrids have been developed towards electrode and electrolyte formation. Future progress on designing efficient three dimensional graphene-MOF hybrids materials may overawe the synthesis, conductivity, and stability challenges towards high performance energy device materials.