The gas turbine engine is an essential component of the global energy infrastructure which accounts for a significant portion of the total fossil fuel consumption in transportation and electric power generation sectors. For this reason there is significant interest in further increasing the efficiency and reducing the pollutant emissions of these devices. Conventional approaches to this goal, which include increasing the compression ratio, turbine inlet temperature, and turbine/compressor efficiency, have brought modern gas turbine engines near the limits of what may be achieved with the conventionally applied Brayton cycle. If a significant future step increase in gas turbine efficiency is to be realized some deviation from this convention is necessary. The pressure gain gas turbine concept is a well established new combustion technology that promises to provide a dramatic increase in gas turbine efficiency by replacing the isobaric heat addition process found in conventional technology with an isochoric process. The thermodynamic benefit of even a small increase in stagnation pressure across a gas turbine combustor translates to a significant increase in cycle efficiency. To date there have been a variety of methods proposed for achieving stagnation pressure gains across a gas turbine combustor and these concepts have seen a broad spectrum of levels of success. The following chapter provides an introduction to one of the proposed pressure gain methods that may be most easily realized in a practical application. This approach, known as pulse combustor driven pressure gain combustion, utilizes an acoustically resonant pulse combustor to approximate isochoric heat release and thus produce a rise in stagnation pressure.