Carbon dioxide (CO2), which results from fossil fuel combustion and industrial processes, accounts for a substantial part of the total anthropogenic greenhouse gases (GHGs). As a result, several carbon capture, utilization and storage (CCUS) technologies have been developed during the last decade. Chemical absorption, adsorption, cryogenic separation and membrane separation are the most widely used post-combustion CO2 capture technologies. This study reviews post-combustion CO2 capture technologies and the latest progress in membrane processes for CO2 separation. More specifically, the objective of the present work is to present the state of the art of membrane-based technologies for CO2 capture from flue gases and focuses mainly on recent advancements in commonly employed membrane materials. These materials are utilized for the fabrication and application of novel composite membranes or mixed-matrix membranes (MMMs), which present improved intrinsic and surface characteristics and, thus, can achieve high selectivity and permeability. Recent progress is described regarding the utilization of metal–organic frameworks (MOFs), carbon molecular sieves (CMSs), nanocomposite membranes, ionic liquid (IL)-based membranes and facilitated transport membranes (FTMs), which comprise MMMs. The most significant challenges and future prospects of implementing membrane technologies for CO2 capture are also presented.