This work presents applications of the probability density function (PDF) method to several recently-developed turbulent flows, and the implementation and assessment of several sub-models. A series of lean piloted premixed jet flames (in order of lowest to highest jet bulk velocity: PM1-50, PM1-100, PM1150, and PM1-200) is first studied using a Reynolds-Averaged Navier-Stokes (RANS) based PDF method. These calculations use diagnostic testing and thorough parametric studies of models to show that the standard models overpredict the reaction rate in the flames PM1-150 and PM1-200. The nature of the combustion in these flames is examined through comparison to simpler combustion models, and it is found to be similar to laminar non-premixed flames. These same flames are then investigated further using both RANS-PDF and the recently developed Large Eddy Simulation (LES) PDF method. Simple models for molecular diffusion and combustion are tested and implemented in the RANS-PDF calculations. In the LES-PDF calculations, the effects of differential diffusion and the mixing model constant, C M , are both examined, and the calculations are found to be very sensitive to the value of C M . This study yields substantially improved calculations of all the flames. In particular, the study of C M shows strong evidence that larger values of C M are necessary for flames PM1-150 and PM1-200. The modeling of molecular mixing is investigated further through a study of a non-reacting turbulent jet flow with three inflowing streams. This study presents the unique opportunity to compare the scalar dissipation rate and conditional diffusion from the calculations to experimental data. In the RANS-PDF calculations of this flow, three classic mixing models are evaluated. The joint scalar PDF's are very sensitive to the choice of mixing model and show a wide variability from the measurements. Only the Euclidean Minimum Spanning Tree (EMST) produces compositions which lie very close to the slow manifold identified in the experimental work. LES calculations of the same flow are performed, and the dissipation rate and conditional diffusion are calculated. The resolved scalar dissipation rate is found to be in good agreement with the experimental data, but depends strongly on the resolution; the total dissipation rate from the RANS-PDF and LES calculations indicates significantly larger scalar dissipation rates than those measured experimentally. Lastly, LES-PDF calculations of the same flow yield joint-PDF's in very good agreement with the experimental data, and are far-improved from those of any mixing model studied with RANS-PDF. The attenuation of variance production model is introduced for LES-PDF and tested in this flow. This new model results in an additional dissipation of scalar variance and yields calculations of improved accuracy on coarse grids.