Post-combustion carbon capture (PCC), which can be retrofitted to existing units in power plants worldwide, is regarded as the first technologically feasible and effective way to combat human-induced climate change. The membrane contactor is an emerging and promising membrane technology for PCC as it integrates the benefits of both liquid absorption (high selectivity) and membrane separation (modularity and compactness). This review aims to provide a state-of-the-art assessment of the research work carried out so far on membrane contactor technology in PCC. It details common aspects of membrane contactors, such as technological advantages, membrane wetting, mass transfer and module design, as well as new advances (e.g., new membranes and absorbents used in absorption processes) and novel applications (e.g., direct CO2 stripping and integrated heat recovery in desorption processes). Moreover, the difference in performance between membrane absorption and conventional absorption is also compared and discussed. Lastly, we discuss the status and progress of membrane contactors in PCC and offer some recommendations for future work. This paper provides a clear overview on the recent developments of membrane contactor technology in PCC.