The carbon dioxide (CO2) crisis is one of the world's most urgent issues. Meeting the worldwide targets set for CO2 capture and storage (CCS) is crucial. Because it may significantly reduce energy consumption compared to traditional amine-based adsorption capture, adsorption dependant CO2 capture is regarded as one of the most hopeful techniques in this paradigm. The expansion of unique, critical edge adsorbent materials has received most of the research attention to date, with the main objective of improving adsorption capacity and lifespan while lowering the temperature of adsorption, thereby lowering the energy demand of sorbent revival. There are specific materials needed for each step of the carbon cycle, including capture, regeneration, and conversion. The potential and efficiency of metal-organic frameworks (MOFs) in overcoming this obstacle have recently been proven through research. In this study, we pinpoint MOFs' precise structural and chemical characteristics that have contributed to their high capture capacity, effective regeneration and separation processes, and efficient catalytic conversions. As prospective materials for the next generation of energy storage and conversion applications, carbon-based compounds like graphene, carbon nanotubes, and fullerenes are receiving a lot of interest. Their distinctive physicochemical characteristics make them suitable for these popular study topics, including structural stability and flexibility, high porosity, and customizable physicochemical traits. It is possible to precisely design the interior of MOFs to include coordinatively unsaturated metal sites, certain heteroatoms, covalent functionalization, various building unit interactions, and integrated nanoscale metal catalysts. This is essential for the creation of MOFs with improved performance. Utilizing the accuracy of MOF chemistry, more complicated materials must be built to handle selectivity, capacity, and conversion all at once to achieve a comprehensive solution. This review summarizes, the most recent developments in adsorption-based CO2 combustion capture, the CO2 adsorption capacities of various classes of solid sorbents, and the significance of advanced carbon nanomaterials for environmental remediation and energy conversion. This review also addresses the difficulties and potential of developing carbon-based electrodes for energy conversion and storage applications.