Carbon dioxide (CO₂) is the single largest contributor to climate change due to its increased emissions since global industrialization began. Carbon Capture, Storage, and Utilization (CCSU) is regarded as a promising strategy to mitigate climate change, reducing the atmospheric concentration of CO₂ from power and industrial activities. Post-combustion carbon capture (PCC) is necessary to implement CCSU into existing facilities without changing the combustion block. In this study, the recent research on various PCC technologies is discussed, along with the membrane technology for PCC, emphasizing the different types of membranes and their gas separation performances. Additionally, an overall comparison of membrane separation technology with respect to other PCC methods is implemented based on six different key parameters—CO₂ purity and recovery, technological maturity, scalability, environmental concerns, and capital and operational expenditures. In general, membrane separation is found to be the most competitive technique in conventional absorption as long as the highly-performed membrane materials and the technology itself reach the full commercialization stage. Recent updates on the main characteristics of different flue gas streams and the Technology Readiness Levels (TRL) of each PCC technology are also provided with a brief discussion of their latest progresses.