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Turbulent combustion in cylinders can be considered to involve chemistry of two different types, namely fast and slow in comparison with the turbulence. Different methods are needed for addressing these two types of chemistry. Turbulent mixing controls the fast chemistry, which proceeds as rapidly as advancing turbulent fronts allow. Slow chemistry is more oblivious to turbulence and proceeds at rates dependent on local temperature, pressure and chemical composition. Reaction-sheet descriptions thus may be applied to fast chemistry and distributed-reaction descriptions to slow. This work addresses methods for describing combustion processes that treat fast and slow chemistry differently. In premixed charges, the principal heat-release rates are fast. Turbulence modeling is suggested to be sufficient for describing the propagation of the main heat-release fronts. Slow chemistry includes autoignition, CO burnup and NOx production.