Though modern low-emission combustion strategies have been successful in abating the emission of pollutants in aircraft engines and power generation gas turbines, combustion instability remains one of the foremost technical challenges in the development of next generation lean premixed combustor technology. Combustion instability is the coupling between unsteady heat release and combustor acoustic modes where one amplifies the other in a feedback loop. This is a complex phenomenon which involves unsteady chemical kinetic, fluid mechanic and acoustic processes that can lead to unstable behavior and could be detrimental in ways ranging from faster part fatigue to catastrophic system failure. Understanding and controlling the onset and propagation of combustion instability is therefore critical to the development of clean and efficient combustion systems. Imaging of combustion radicals has been a cornerstone diagnostic for the field of combustion for the past two decades which allows for visualization of flame structure and behavior. However, resolving both temporal and spatial structures from image-based experimental data can be very challenging. Thus, understanding flame dynamics remains a demanding task and the difficulties often lie in the chaotic and non-linear behavior of the system of interest. To this end, this work investigates the flame dynamics of lean premixed swirl stabilized flames in two distinct configurations using a variety of high fidelity optical and laser diagnostic techniques in conjunction with advanced data / algorithm based post-processing tools.The first part of this work is focused on establishing the effectiveness of microwave plasma discharges in improving combustor flame dynamics through minimizing heat release and pressure fluctuations. The effect of continuous, volumetric, direct coupled, non-equilibrium, atmospheric microwave plasma discharge on a swirl stabilized, lean premixed methane˗air flame was investigated using quantitative OH planar laser induced fluorescence (PLIF), spectrally resolved emission and acoustic pressure measurements. Proper Orthogonal Decomposition (POD) was used to post-process OH-PLIF images to extract information on flame dynamics that are usually lost through classical statistical approaches. Results show that direct plasma coupling accelerates combustion chemistry due to the non-thermal effects of plasma that lead to significantly improved combustor dynamics. Overall, this study demonstrates that microwave direct plasma coupling can drastically enhance dynamic flame stability of swirl stabilized flames especially at very lean operating conditions.The second part of this work is focused on the development of a stable and efficient small-scale combustor architecture with comparable power density, performance and emission characteristics to that of existing large-scale burners with reduced susceptibility to extinction and externally imposed acoustic perturbations while maintaining high combustion efficiency and low emission levels under ultra-lean operating conditions. Prototype burner arrays were additively manufactured, and the combustion characteristics of the mesoscale burner array were studied using several conventional and optical diagnostic techniques. The burner array was specifically configured to enhance overall combustion stability, particularly under lean operating conditions, by promoting flame to flame interactions between the neighboring elements. Dynamic mode decomposition (DMD) analysis based on high speed OH-PLIF images was carried out to provide a quantitative measure of flame stability. Results show a marked improvement in combustion stability for a mesoscale burner array compared to a single swirl-stabilized flame with similar power output. Overall, this study shows promise for integration of mesoscale combustor arrays as a flexible and scalable technology in next generation propulsion and power generation systems.