In this article, we present a comprehensive review and numerical analysis of liquid oxygen (LOx)-methane (CH<sub>4</sub>) combustion at supercritical pressures. A detailed review of numerical and experimental investigations on LOx-CH<sub>4</sub> combustion was conducted to understand the transcritical injection and supercritical combustion process occurring in a typical high-pressure rocket engine. In this work, we performed comprehensive numerical tests using statistical models, such as steady laminar flamelet (SLF) and flamelet/progress variable [flamelet-generated manifold (FGM)], and the kinetic approach of eddy dissipation concept (EDC) combustion closure to develop an accurate but computationally efficient supercritical combustion modeling methodology. A benchmark ONERA Mascotte chamber [G2 RCM-3 (V04)] test case was utilized to simulate LOx-CH<sub>4</sub> combustion. A systematic study of three different combustion models with different step chemical kinetic mechanisms was performed to identify the role of the detailed and reduced chemical mechanisms. The results of the study showed the efficacy of the FGM framework, which incorporates finite-rate kinetics in the LOx-CH<sub>4</sub> turbulent diffusion flame. The simulated flame shape and peak temperature location closely matched the G2 test observation. The kinetic model study revealed that the reduced mechanism can also describe the flame structure accurately in the FGM framework. The FGM model reproduced the experimental flame structure and hydroxyl concentration accurately compared to the SLF and EDC models. This study highlights the importance of finite-rate effects in LOx-CH<sub>4</sub> combustion and reveals that the statistical turbulence-chemistry approach of the FGM model is accurate and computationally less expensive for sub-scale or full-scale LOx-CH<sub>4</sub> rocket engine simulations.