Biogas is a sustainable energy source produced mostly from municipal wastewater treatment plants, landfills, and agricultural sources, mainly manure and energy crops, through the anaerobic digestion process. The major components of biogas are methane (CH4) and carbon dioxide (CO2), with small proportions of hydrogen sulfide (H2S), ammonia (NH3), hydrogen (H2), nitrogen (N2), carbon monoxide (CO), and oxygen (O2). However, impurities in the form of CO2 gas should be removed prior to commercial use of biogas to harness the maximum energy and increase the calorific value. Several purification processes have been developed, including chemical and physical absorption, pressure swing adsorption (PSA), cryogenic separation, and membrane technologies. Whereas substantial progress has been made in the field of FTMs for CO2 separations over the years, which makes FTMs one of the most promising technology for biogas upgradation. Therefore, this chapter is mainly focused on the thorough review of different types of FTMs and their recent progress for the biogas purification application, which includes the details of different membrane structural details, fabrication method for both FTMs and carriers, and various parameters that influence the CO2/CH4 separation performance. In addition, the permeability-selectivity trade-off Robeson�s upper bound graph that demonstrate the CO2/CH4 performance of different FTMs for biogas purification is also discussed in this literature. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.