Trapped Vortex Combustor (TVC) is a relatively new concept for potential use in gas turbine engines addressing ever increasing demands of high efficiency, low emissions, low pressure drop, and improved pattern factor. This concept holds promise for future because of its inherent advantages over conventional swirl-stabilized combustors. The main difference between TVC and a conventional gas turbine combustor is in the way combustion is stabilized. In conventional combustors, flame is stabilized because of formation of toroidal flow pattern in the primary zone due to interaction between incoming swirling air and fuel flow. On the other hand, in TVC, there is a physical cavity in the wall of combustor with continuous injection of air and fuel leading to stable and sustained combustion. Past work related to TVC has focussed on use of two cavities in the combustor liner. In the present study, a single cavity combustor concept is evaluated through simulation and experiments for applications requiring compact combustors such as Unmanned Aerial Vehicles (UAVs) and cruise missiles. In the present work, numerical simulations were initially performed on a planar, rectangular single-cavity geometry to assess sensitivity of various parameters and to design a single-cavity TVC test rig. A water-cooled, modular, atmospheric pressure TVC test rig is designed and fabricated for reacting and non-reacting flow experiments. The unique features of this rig consist of a continuously variable length-to-depth ratio (L/D) of the cavity and optical access through quartz plates provided on three sides for visualization. Flame stabilization in the single cavity TVC was successfully achieved with methane as fuel, and the range of flow conditions for stable operation were identified. From these, a few cases were selected for detailed experimentation. Reacting flow experiments for the selected cases indicated that reducing L/D ratio and increasing cavity-air velocity favour stable combustion. The pressure drop across the single-cavity TVC is observed to be lower as compared to conventional combustors. Temperatures are measured at the exit using thermocouples and corrected for radiative losses. Species concentrations are measured at the exit using an exhaust gas analyzer. The combustion efficiency is observed to be around 98-99% and the pattern factor is observed to be in the range of 0.08 to 0.13. High-speed imaging made possible by the optical access indicates that the overall combustion is fairly steady, and there is no major vortex shedding downstream. This enabled steady-state simulations to be performed for the selected cases. Insight from simulations has highlighted the importance of air and fuel injection strategies in the cavity. From a mixing and combustion efficiency standpoint, it is desirable to have a cavity vortex that is anti-clockwise. However, the natural tendency for flow over a cavity is to form a vortex that is clockwise. The tendency to blow-out at higher inlet flow velocities is thought to be because of these two opposing effects. This interaction helps improve mixing, however leads to poor flame stability unless cavity-air velocity is strong enough to support a strong anti-clockwise vortex in the cavity. This basic understating of cavity flow dynamics can be used for further design improvements in future to improve flame stability at higher inlet flow velocities and eventually lead to the development of a practical combustor.