A comprehensive theoretical/numerical framework has been established to treat the combustion of liquid oxygen (LOX) and methane under supercritical conditions. The model accounts for detailed LOX/methane reaction mechanisms, and accommodates the effect of scalar dissipation on finite-rate chemistry. Turbulence closure is achieved by a large-eddy simulation technique. Several different turbulent combustion models are implemented and assessed by comparing the chemical and turbulence time scales at conditions typical of liquid-propellant engine rocket operation. Results indicate that the flamelet assumption is appropriate. The direct-closure approach may over-predict the reaction rate. The supercritical mixing and combustion LOX and methane downstream of a splitter are analyzed systemically, and the effects of real-fluid thermodynamics on the cryogenic-fluid flame evolution are quantified.