A transported probability density function (PDF) model is used to simulate the in-cylinder combustion processes in a compression-ignition heavy-duty engine. Heavy-duty vehicles are substantial users of petroleum-based fuels and significant contributors to greenhouse-gas emissions. For these reasons, it is essential to improve the efficiency and reduce the emissions in compression-ignition engines. Several advanced combustion strategies have been explored recently with the goal of decreasing the fuel consumption in compression-ignition engines for heavy-duty vehicles. These strategies include higher pressures, lower temperatures, varying degrees of fuel/air premixing and/or multiple fuels. Therefore, the combustion model should be able to deal with mixed-mode turbulent combustion under widely varying thermochemical conditions and should also be able to accommodate the use of multiple fuels and arbitrary numbers of liquid fuel injection events per engine cycle. The transported PDF model has the distinct advantage of handling all these conditions in a direct manner with minimal approximations. In this paper, recent results from in-cylinder combustion simulations using the transported PDF model for several operating conditions for a heavy-duty engine are presented. The computed pressure traces agree reasonably well with experimental data and respond correctly to variations in engine operating conditions. More importantly, significant differences are found between the results obtained using the transported PDF model that explicitly accounts for the turbulence/chemistry interactions (TCI) and those obtained using a model that do not account for TCI. Marked differences are observed in the computed flame structure and the global quantities between the two models. These differences indicate the extent to which unresolved turbulent fluctuations in composition and temperature influence the mean chemical reaction rates in a compression-ignition heavy-duty engine.