In today’s world, owing to industrial expansion, urbanization, the rapid growth of the human population, and the high standard of living, the utilization of the most advanced technologies is unavoidable. The enhanced anthropogenic activities worldwide result in a continuous increase in global warming potential, thereby raising a global concern. The constant rise in global warming potential forces the world to mitigate greenhouse gases, particularly carbon dioxide. Carbon dioxide is considered as the primary contributor responsible for global warming and climatic changes. The global anthropogenic carbon dioxide emissions released into the atmosphere can eventually deteriorate the environment and endanger the ecosystem. Combating global warming is one of the main challenges in achieving sustainable development. Carbon capture and storage is a potential solution to mitigate carbon dioxide emissions. There are three main methods for carbon capture and storage: post-combustion, pre-combustion, and oxy-fuel combustion. Among them, post-combustion is used in thermal power plants and industrial sectors, all of which contribute a significant amount of carbon dioxide. Different techniques such as physical and chemical absorption, physical and chemical adsorption, membrane separation, and cryogenic distillation used for carbon capture are thoroughly discussed and presented. Currently, there are various materials including absorbents, adsorbents, and membranes used in carbon dioxide capture. Still, there is a search for new and novel materials and processes for separating and capturing carbon dioxide. This review article provides a comprehensive review of different methods, techniques, materials, and processes used for separating and capturing carbon dioxide from significant stationary point sources.