The use of fossil fuel is expected to increase significantly by midcentury because of the large rise in the world energy demand despite the effective integration of renewable energies in the energy production sector. This increase, alongside with the development of stricter emission regulations, forced the manufacturers of combustion systems, especially gas turbines, to develop novel combustion techniques for the control of NOx and CO2 emissions, the latter being a greenhouse gas responsible for more than 60% to the global warming problem. The present review addresses different burner designs and combustion techniques for clean power production in gas turbines. Combustion and emission characteristics, flame instabilities, and solution techniques are presented, such as lean premixed air-fuel (LPM) and premixed oxy-fuel combustion techniques, and the combustor performance is compared for both cases. The fuel flexibility approach is also reviewed, as one of the combustion techniques for controlling emissions and reducing flame instabilities, focusing on the hydrogen-enrichment and the integrated fuel-flexible premixed oxy-combustion approaches. State-of-the-art burner designs for gas turbine combustion applications are reviewed in this study, including stagnation point reverse flow (SPRF) burner, dry low NOx (DLN) and dry low-emission (DLE) burners, EnVironmental burners (including EV, AEV, and SEV burners), perforated plate (PP) burner, and micromixer (MM) burner. Special emphasis is made on the MM combustor technology, as one of the most recent advances in gas turbines for stable premixed flame operation with wide turndown and effective control of NOx emissions. Since the generation of pure oxygen is prerequisite to oxy-combustion, oxygen-separation membranes became of immense importance either for air separation for clean oxy-combustion applications or for conversion/splitting of the effluent CO2 into useful chemical and energy products. The different carbon-capture technologies, along with the most recent carbon-utilization approaches towards CO2 emissions control, are also reviewed.