Carbon dioxide (CO2) is one of the most abundant greenhouse gases in Earth's atmosphere and responsible for global warming. Therefore, aerial CO2 capture and sequestration has become a major task for human community. Though several adsorbents for CO2 including activated carbon, zeolites, metal-organic frameworks (MOFs), and other surface-modified porous materials are well developed, the supramolecular approaches using synthetic hydrogen-bonding receptors are less explored. This review article highlights the synthetic development of various artificial receptors and their properties toward fixation of aerial CO2 as carbonate (CO3 2-), bicarbonate (HCO3 -), or carbamate (-NHCOO-/>NCOO-) ions, induced by excess fluoride (F-) or hydroxide (OH-) ions as their tetrabutylammonium salts. The utilization of encapsulated carbonate/bicarbonate/carbamate complexes in anion exchange metathesis for separation of oxyanions from aqueous solutions are also discussed. In addition, the release of CO2 and regeneration of receptor molecules are described in a number of occasions. Most importantly, the formation of anion complexes as crystalline materials in solid-state is described in terms of supramolecular chemistry and correlated with their solution-state properties. Finally, the types of receptors containing various functional groups are scrutinized in CO2 uptake, storage, and release processes and hints of endeavours for future research are delineated.