Marine plastic debris floating on the ocean surface is a major environmental problem. However, its distribution in the ocean is poorly mapped, and most of the plastic waste estimated to have entered the ocean from land is unaccounted for. Better understanding of how plastic debris is transported from coastal and marine sources is crucial to quantify and close the global inventory of marine plastics, which in turn represents critical information for mitigation or policy strategies. At the same time, plastic is a unique tracer that provides an opportunity to learn more about the physics and dynamics of our ocean across multiple scales, from the Ekman convergence in basin-scale gyres to individual waves in the surfzone. In this review, we comprehensively discuss what is known about the different processes that govern the transport of floating marine plastic debris in both the open ocean and the coastal zones, based on the published literature and referring to insights from neighbouring fields such as oil spill dispersion, marine safety recovery, plankton connectivity, and others. We discuss how measurements of marine plastics (both in situ and in the laboratory), remote sensing, and numerical simulations can elucidate these processes and their interactions across spatio-temporal scales. Environ. Res. Lett. 15 (2020) 023003 E van Sebille et al Environ. Res. Lett. 15 (2020) 023003 E van Sebille et al References Acha E M, Mianzan H W, Iribarne O, Gagliardini D A, Lasta C and Daleo P 2003 The role of the Rı́o de la Plata bottom salinity front in accumulating debris Mar. Pollut. Bull. 46 197-202 Acha E M, Piola A, Iribarne O and Mianzan H 2015 Ecological Processes at Marine Fronts: Oases in the Ocean (Berlin: Springer) Aliani S and Molcard A 2003 Hitch-hiking on floating marine debris: macrobenthic species in the Western Mediterranean Sea Hydrobiologia 503 59-67 Allen J 1985 Principles of Physical Sedimentology (Berlin: Springer) Alpers W 1985 Theory of radar imaging of internal waves Nature 314 245-7 Alsina J M and Cáceres I 2011 Sediment suspension events in the inner surf and swash zone. Measurements in large-scale and high-energy wave conditions Coast. Eng. 58