High efficiency, low emissions and stable operation over a wide range of conditions are some of the key requirements of modem-day combustors. To achieve these objectives, lean premixed flames are generally preferred as they achieve efficient and clean combustion. A drawback of lean premixed combustion, however, is that the flames are more prone to dynamics. The unsteady release of sensible heat and flow dilatation in combustion processes create pressure fluctuations which, particularly in premixed flames, can couple with the acoustics of the combustion system. This acoustic coupling creates a feedback loop with the heat release that can lead to severe thermoacoustic instabilities that can damage the combustor. Understanding these dynamics, predicting their onset and proposing passive and active control strategies are critical to large-scale implementation. For the numerical study of such systems, large eddy simulation (LES) techniques with appropriate combustion models and reaction mechanisms are highly appropriate. These approaches balance the computational complexity and predictive accuracy. This work, therefore, aims to explore the applicability of these methods to the study of premixed wake stabilized flames. Specifically, finite rate chemistry LES models that can effectively capture the interaction between different turbulent scales and the combustion fronts have been implemented, and applied for the analysis of premixed turbulent flame dynamics in laboratory-scale combustor configurations. Firstly, the artificial flame thickening approach, along with an appropriate reduced chemistry mechanism, is utilized for modeling turbulence-combustion interactions at small scales. A novel dynamic formulation is proposed that explicitly incorporates the influence of strain on flame wrinkling by solving a transport equation for the latter rather than using local-equilibrium-based algebraic models. Additionally, a multiple-step combustion chemistry mechanism is used for the simulations. Secondly, the presumed-PDF approach, coupled with the flamelet generated manifold (FGM) technique, is also implemented for modeling turbulence-combustion interactions. The proposed formulation explicitly incorporates the influence of strain via the scalar dissipation rate and can result in more accurate predictions especially for highly unsteady flame configurations. Specifically, the dissipation rate is incorporated as an additional coordinate to presume the PDF and strained flamelets are utilized to generate the chemistry databases. These LES solvers have been developed and applied for the analysis of reacting flows in several combustor configurations, i.e. triangular bluff body in a rectangular channel, backward facing step configuration, axi-symmetric bluff body in cylindrical chamber, and cylindrical sudden expansion with swirl, and their performance has been be validated against experimental observations. Subsequently, the impact of the equivalence ratio variation on flame-flow dynamics is studied for the swirl configuration using the experimental PIV data as well as the numerical LES code, following which dynamic mode decomposition of the flow field is performed. It is observed that increasing the equivalence ratio can appreciably influence the dominant flow features in the wake region, including the size and shape of the recirculation zone(s), as well as the flame dynamics. Specifically, varying the heat loading results in altering the dominant flame stabilization mechanism, thereby causing transitions across distinct- flame configurations, while also modifying the inner recirculation zone topology significantly. Additionally, the LES framework has also been applied to gain an insight into the combustion dynamics phenomena for the backward-facing step configuration. Apart from evaluating the influence of equivalence ratio on the combustion process for stable flames, the flame-flow interactions in acoustically forced scenarios are also analyzed using LES and dynamic mode decomposition (DMD). Specifically, numerical simulations are performed corresponding to a selfexcited combustion instability configuration as observed in the experiments, and it is observed that LES is able to suitably capture the flame dynamics. These insights highlight the effect of heat release variation on flame-flow interactions in wall-confined combustor configurations, which can significantly impact combustion stability in acoustically-coupled systems. The fidelity of the solvers in predicting the system response to variation in heat loading and to acoustic forcing suggests that the LES framework can be suitably applied for the analysis of flame dynamics as well as to understand the fundamental mechanisms responsible for combustion instability. KEY WORDS - large eddy simulation, LES, wake stabilized flame, turbulent premixed combustion, combustion modeling, artificially thickened flame model, triangular bluff body, backward facing step combustor, presumed-PDF model, flamelet generated manifold, axi-symmetric bluff body, cylindrical swirl combustor, particle image velocimetry, dynamic mode decomposition, combustion instability, forced response.