AbstractMax-pressure control is a new approach to signal timing with mathematically proven network throughput properties. Over the past decade, max-pressure control has emerged from a novel mathematical idea in a simple store-and-forward queueing model to include practical aspects like a signal cycle, realistic traffic flow models, measurement errors, and intersection access for alternative modes. Furthermore, max-pressure control is adaptive to local queues and to changes in network demand. Max-pressure control is also decentralized and easy to compute. A broad range of numerical results in calibrated microsimulation models have mostly demonstrated superior performance from max-pressure control compared with existing signal timing methods, and some researchers have started to experiment with max-pressure control on actual roads. Given these benefits, the purpose of this review paper is to provide a summary of the mathematical approach, methodological improvements, and numerical results. This summary is intended for researchers interested in continuing methodological or numerical work and for practitioners exploring the potential use of this state-of-the-art signal timing method.