Recently, natural gas-fired power generation has attracted more attention as it has lower specific CO2 emissions and higher operational flexibility than coal- and oil-fired power generation. In state-of-the-art gas-fired oxy-combustion cycles, combustion takes place at elevated pressure, which enables high efficiency and competitive economic performance. This review presents a new insight by summarising the main challenges associated with these types of cycles and covers: (i) O2 production methods and purity; (ii) types of exhaust gas recirculation; and (iii) operating pressure. The techno-economic evaluation of the state-of-the-art gas-fired power cycles showed that although the Allam cycle is superior among other cycles with an efficiency of 55.1%, its highly affected levelised cost of electricity by interest rate adds more uncertainty to investment decisions. Importantly, the progress towards the next generation of gas-fired oxy-combustion cycles will require the development of less complex cycles with more efficient and less energy-intensive O2 production.