This thesis investigates the localized and global extinction in turbulent swirling non-premixed flames with Large Eddy Simulation (LES) and sub-grid scale Conditional Moment Closure (CMC) model. The first part of this thesis describes the derivations of the three dimensional conservative CMC governing equations and their finite volume discretization for unstructured mesh. The parallel performance of the newly developed CMC code is assessed. The runtime data coupling interface between the 3D-CMC and LES solvers is designed and the different solvers developed during the course of this research are detailed. The aerodynamics of two swirling non-reacting flows from the Sydney and Cambridge burners are first simulated. The main ow structures (e.g. the recirculating zones) in both cases are correctly predicted. The sensitivity analysis about the influences of turbulent inlet boundary, computational domain and mesh refinement on velocity statistics is conducted. This analysis acts as the preparatory investigation for the following flame simulations. The Sydney swirl diluted methane flame, SMA2, is then simulated for validating the LES/3D-CMC solvers. Excellent agreements are achieved in terms of velocity and mixture fraction statistics, averaged reactive scalars in both physical and mixture fraction space. The local extinction level from the increased central fuel velocity is reasonably predicted. At the experimental blow-off point, the LES/3D-CMC modelling does not obtain the occurrence of complete extinction, but severe extinction occurs at the flame base, qualitatively in line with experimental observations. Localized extinction features of a non-premixed methane flame in the Cambridge swirl burner are investigated and it is found that the occurrence of local extinction is typically manifested by low heat release rate and hydroxyl mass fraction, as well as low or medium temperature. It is also accompanied by high scalar dissipation rates. In mixture fraction space, the CMC cells undergoing local extinction have relatively wide scatter between inert and fully burning solutions. The PDFs of reactedness at the stoichiometric mixture fraction demonstrate some extent of bimodality, showing the events of local extinction and reignition and their relative occurrence frequency. Local extinction near the bluff body in the Cambridge swirl burner is also studied. The convective wall heat loss is included as a source term in the conditionally filtered total enthalpy equation. It shows a significant influence on the mean flame structures, directly linked to the changes of the conditional scalar dissipation near the wall. Furthermore, the degree of local extinction near the bluff body surface is intensified because of the wall heat loss. However, the wall heat loss shows a relatively small influence on the statistics of lift-off height. Finally, the blow-off conditions and dynamics in the Cambridge swirl burner are investigated. The blow-off critical air bulk velocity from LES/3D-CMC is over-predicted, greater than the experimental one by at most 25%. The predicted blow-off transient lasts finitely long duration quantified by the blow-off time, in good agreement with the experimental results. The reactive scalars in both physical and mixture fraction space demonstrate different transient behaviors during blow-off process. When the current swirling flame is close to blow-off, high-frequency and high-amplitude fluctuations of the conditionally filtered stoichiometric scalar dissipation rate on the iso-surfaces of the filtered stoichiometric mixture fraction are evident. The blow-off time from the computations is found to vary with different operating conditions.