Irradiating a flame via microwave radiation is a plasma-assisted combustion (PAC) technology that can be used to modify the combustion chemical kinetics in order to improve flame stability and to delay lean blow-out. One practical implication is that combustion engines may be able to operate with leaner fuel mixtures and have an improved fuel flexibility capability including biofuels. Furthermore, this technology may assist in reducing thermoacoustic instabilities, which is a phenomenon that may severely damage the engine and increase NOX production. To further understand microwave-assisted combustion, a skeletal kinetic reaction mechanism for methane air combustion is developed and presented. The mechanism is detailed enough to take into account relevant features, but sufficiently small to be implemented in large eddy simulations (LES) of turbulent combustion. The mechanism consists of a proposed skeletal methane air reaction mechanism accompanied by subsets for ozone, singlet oxygen, chemionization, and electron impact reactions. The baseline skeletal methane air mechanism contains 17 species and 42 reactions, and it predicts the ignition delay time, flame temperature, flame speed, major species, and most minor species well, in addition to the extinction strain, compared to the detailed GRI 3.0 reaction mechanism. The amended skeletal reaction mechanism consists of 27 species and 80 reactions and is developed for a reduced electric field E/N below the critical, field strength (of similar to 125 Td) for the formation of a microwave breakdown plasma. Both laminar and turbulent flame simulation studies are carried out with the proposed skeletal reaction mechanism. The turbulent flame studies consist of propagating planar flames in homogeneous isotropic turbulence in the reaction sheets and the flamelets in eddies regimes, and a turbulent low-swirl flame. A comparison with experimental data is performed for a turbulent low-swirl flame. The results suggest that we can influence both laminar and turbulent flames by nonthermal plasmas, based on microwave irradiation. The laminar flame speed increases more than the turbulent flame speed, but the radical pool created by the microwave irradiation significantly increases the lean blow-out limits of the turbulent flame, thus making it less vulnerable to thermoacoustic combustion oscillations. Apart from the experimental results from low-swirl flame presented here, experimental data for validation of the simulated trends are scarce, and conclusions build largely on simulation results. Analysis of chemical kinetics from simulations of laminar flames and LES on turbulent flames reveal that singlet oxygen molecule is of key importance for the increased reactivity, accompanied by production of radicals such as O and OH.