Covalent organic frameworks (COFs) are highly crystalline polymers that possess exceptional porosity and surface area, making them a subject of significant research interest. COF materials are synthesized by chemically linking organic molecules in a repetitive arrangement, creating a highly effective porous crystalline structure that adsorbs and retains gases. They are highly effective in removing impurities, such as CO2, because of their desirable characteristics, such as durability, high reactivity, stable porosity, and increased surface area. This study offers a background overview, encompassing a concise discussion of the current issue of excessive carbon emissions, and a synopsis of the materials most frequently used for CO2 collection. This review provides a detailed overview of COF materials, particularly emphasizing their synthesis methods and applications in carbon capture. It presents the latest research findings on COFs synthesized using various covalent bond formation techniques. Moreover, it discusses emerging trends and future prospects in this particular field.