In a conventional gas-turbine engine, fuel is burned in separate combustors before the heated high-pressure gas expands through the turbine to provide shaft power for the compressor, fan, propellers, helicoptor rotors, or an electric generator in a ground-based powerplant application. It is proposed in this paper that combustion be continued purposely inside the turbine to increase the efficiency and specific thrust/power of the engine. We term such a turbine with combustion a turbine-burner. A thermodynamic cycle analysis is performed to demonstrate the performance gains of turbojet engines with the turbine burner over the conventional turbojets. Ground-based gas-turbine engines for power generation are also analyzed, with the results showing even better performance gains compared without conventional engines. A mixing-layer analysis with combustion in an accelarated flow similar to the conditions in the turbine burner shows that there is also potential reduction of NOx by using the turbine-burner compared with conventional combustors, where the burning is at a constant pressure. Challenges and related research issues that must be addressed to use the turbine-burner technology are identified in this paper.