Transported probability density function (PDF) methods are used to simulate liquid fuel injection (n-heptane), vaporization, mixing, autoignition, and combustion for a constant-volume combustion chamber under diesel-engine-like conditions. Both stochastic Lagrangian particle and stochastic Eulerian field methods are used to solve the modeled PDF transport equation. Model results are compared with experimental measurements for nonreacting vaporizing sprays and for cases with autoignition and combustion. Parametric studies of the influences of key physical and numerical parameters are performed to establish sensitivities. The model generally captures the measured trends in ignition timing and liftoff length with variations in the thermochemical environment. The most important finding is that there are large differences between results from simulations that include the transported PDF method and those from simulations that ignore local turbulent fluctuations in composition and temperature. This underscores the importance of accounting explicitly for turbulence-chemistry interactions in simulations of autoignition and combustion in compression-ignition engines.