Plastics and other artificial materials pose new risks to the health of the ocean. Anthropogenic debris travels across large distances and is ubiquitous in the water and on shorelines, yet, observations of its sources, composition, pathways, and distributions in the ocean are very sparse and inaccurate. Total amounts of plastics and other man-made debris in the ocean and on the shore, temporal trends in these amounts under exponentially increasing production, as well as degradation processes, vertical fluxes, and time scales are largely unknown. Present ocean circulation models are not able to accurately simulate drift of debris because of its complex hydrodynamics. In this paper we discuss the structure of the future integrated marine debris observing system (IMDOS) that is required to provide long-term monitoring of the state of this anthropogenic pollution and support operational activities to mitigate impacts on the ecosystem and on the safety of maritime activity. The proposed observing system integrates remote sensing and in situ observations. Also, models are used to optimize the design of the system and, in turn, they will be gradually improved using the products of the system. Remote sensing technologies will provide spatially coherent coverage and consistent surveying time series at local to global scale. Optical sensors, including high-resolution imaging, multi- and hyperspectral, fluorescence, and Raman technologies, as well as SAR will be used to measure different types of debris. They will be implemented in a variety of platforms, from hand-held tools to ship-, buoy-, aircraft-, and satellite-based sensors. A network of in situ observations, including reports from volunteers, citizen scientists and ships of opportunity, will be developed to provide data for calibration/validation of remote sensors and to monitor the spread of plastic pollution and other marine debris. IMDOS will interact with other observing systems monitoring physical, chemical, and biological processes in the ocean and on shorelines as well as the state of the ecosystem, maritime activities and safety, drift of sea ice, etc. The synthesized data will support innovative multi-disciplinary research and serve a diverse community of users.