Surface waters of the oceans carry large amounts of material, including sediment grains, plankton organisms, ice crystals, as well as pollutants, e.g., oil and plastic. Transport and spatio-temporal distribution of that material depend on its properties and on the dynamical processes in the ocean mixed layer – currents, waves, turbulence, and convective mixing – acting at a wide range of scales. Due to its importance for marine physics, biogeochemistry and ecology, substantial research effort has been put in recent years into observations and modelling of ocean material transport, especially in the context of marine plastic pollution. Nevertheless, many important questions remain unanswered. In this work, numerically simulated trajectories of surface-floating particles in the period 1993–2020 are used to analyze usual and anomalous transport pathways in the northern North Atlantic and the Arctic Ocean. Lagrangian trajectories are computed based on surface currents from a hydrodynamic model and Stokes drift from a spectral wave model. It is shown that due to high amplitudes of Stokes drift (comparable with wind-induced currents in ice-free parts of the domain of study), combined with its high directional variability, it substantially modifies the drifting paths, underlying the important role of wave-induced currents in surface material transport. A statistical analysis of ∼1.6·108 trajectories reveals patterns of connections between nearshore locations in the domain of study, the associated drift times and path sinuosity. Seasonal variability of transport, different in the Arctic Ocean and the North Atlantic, is found for typical transport routes following the larger-scale circulation patterns. Crucially, in both sub-domains episodic, but very strong transport events between otherwise isolated locations occur, associated with anomalous atmospheric circulation and, arguably, providing ‘windows of opportunity’ for dispersal of various organisms to new locations. It is shown for two examples in the North Atlantic region that an unusual combination of atmospheric circulation indices explains the anomalous transport, thus providing a predictive tool for future events. In the Arctic, analogous phenomena are modified by the state of the sea ice cover.