We present the Sounds of New York City (SONYC) project, a smart cities initiative focused on developing a cyber-physical system for the monitoring, analysis and mitigation of urban noise pollution. Noise pollution is one of the topmost quality of life issues for urban residents in the U.S. with proven effects on health, education, the economy, and the environment. Yet, most cities lack the resources to continuously monitor noise and understand the contribution of individual sources, the tools to analyze patterns of noise pollution at city-scale, and the means to empower city agencies to take effective, data-driven action for noise mitigation. The SONYC project advances novel technological and socio-technical solutions that help address these needs. SONYC includes a distributed network of both sensors and people for large-scale noise monitoring. The sensors use low-cost, low-power technology, and cutting-edge machine listening techniques, to produce calibrated acoustic measurements and recognize individual sound sources in real time. Citizen science methods are used to help urban residents connect to city agencies and each other, understand their noise footprint, and facilitate reporting and self-regulation. Crucially, SONYC utilizes big data solutions to analyze, retrieve and visualize information from sensors and citizens, creating a comprehensive acoustic model of the city that can be used to identify significant patterns of noise pollution. These data can be used to drive the strategic application of noise code enforcement by city agencies to optimize the reduction of noise pollution. The entire system, integrating cyber, physical and social infrastructure, forms a closed loop of continuous sensing, analysis and actuation on the environment. SONYC provides a blueprint for the mitigation of noise pollution that can potentially be applied to other cities in the US and abroad.