This research concerns the application of the Probability Density Function (PDF) on Large Eddy Simulations (LES) of turbulent reacting flows in a wide range of open flame configurations spanning between the premixed and non-premixed regime. The aim is to validate the applicability of the PDF model on a wide range of flames without any special treatment. Additionally, the \textit{a-posteriori} Chemical Exposive Mode Analysis (CEMA) has been applied to the results in order to examine the flame structure and identify locations of extinction, re-ignition, etc. Four different series of flames are studied, each one of them belonging to a completely different combustion regime. The F1-F3 premixed turbulent flames is the first family of flames where the PDF method is applied. The LES-PDF model is shown to accurately predict the flow field and the scalar field even on a very coarse grid. The simulations were performed on a personal computer, so the computational power was severely restricted. Nevertheless, the PDF model was able to give accurate predictions, so one of the flames was chosen for a further sensitivity analysis. A large number of modelling parameters were studied and the results show little sensitivity to them in contrast to RANS-PDF approaches in premixed flames. Finally, the model is able to capture large scale quenching at qualitatively the correct extinction speed. The Cambridge-Sandia series of swirling stratified flames was also examined. It encompasses a wide range of flames with various combinations of swirl and stratification ratio levels. Four distinct cases were selected and tested. For the most simple flames (SwB1 and SwB5), the model gives excellent prediction for both the flow field and the scalar distribution. The introduction of the additional fields improves slightly the results, especially at locations further away from the nozzle exit. For the flames which exhibit more complex flow fields and complex characteristics (SwB6 and SwB11), the model gives reasonable results, given the complexity of the flow field. The introduction of differential diffusion and heat losses towards the ceramic cap was studied independently on the SwB11 flame and was found to have counteracting effects. Therefore, their combination was tested and was found to give a significant improvement. The next series of flames is the Sydney Swirl flames. The SM1 and SM2 flames are two complex swirling flames with a difficult flow field to capture. The field is composed of recirculating zones and vortex break-down bubble areas. The SM2 has not been tested in the literature and this work is the first modelling approach. The flow field simulation results are reasonable, given the complexity of the flame. The biggest discrepancies are observed close to the nozzle exit. The Chemical Explosive Mode Analysis is also performed to give information about the flame structure. The flame is divided into three distinct zones with the second one being a very large quenching region. The CEMA analysis explains why the flame does not quench, but re-ignites further down. Finally, the Delft III premixed flame is studied, a difficult flame to model as it shows quenching with large extinction pockets despite the moderately low Reynolds number. The major flow characteristics were accurately captured by the simulation and the introduction of the additional stochastic fields improves the results close to the nozzle exit. Contrary to most researchers that model the pilot flow as a single heat source close to the nozzle exit, in this work the pilot flow is modelled as a separate flow stream, something that increased the complexity of the simulations due to the extremely thin pilot rim which was comparable to the cell size. Nevertheless, the model was able to accurately capture the localized extinction throughout the flame and the application of the Chemical Explosive Mode Analysis gave further insight into the structure of the flame.