Climate change is because of increase in global temperatures, known as global warming, which is largely attributed to the rising levels of greenhouse gases in the atmosphere, with carbon dioxide emissions from fossil fuel power plants being the major culprit. To effectively mitigate climate change, it is essential to implement carbon capture, utilization, and storage (CCUS) strategies. However, the complexity and diverse range of emission sources, which vary in terms of volume, composition, location, type, and industry, demands a multifaceted strategy that involves the development of a broad spectrum of carbon capture and storage (CCS) technologies, materials, and processes. This review article provides an in-depth review of the three dominant material types utilized globally for CO2 capture from flue gases: Absorbents, Membranes, and Adsorbents (AMA). The author examines the benefits and drawbacks of employing different forms of AMA in post-combustion capture, highlighting recent breakthroughs in experimental and theoretical modeling, simulation, and optimization studies. The review also explores the strengths and limitations of various AMA configurations, including single-stage, multi-stage, and hybrid systems, identifying knowledge gaps and opportunities for advancement in this field. While two-stage hybrid configurations have emerged as the most promising approach to maximizing CO2 recovery, energy efficiency, and cost savings; however, further in-depth techno-economic evaluations are required to determine the most effective and viable configuration within this hybrid category, to pinpoint the optimal solution for real-world applications.