The transport of radionuclides at oceanic scales can be assessed using a Lagrangian model. In this review an application of such a model to the Atlantic, Indian and Pacific oceans is described. The transport model, which is fed with water currents provided by global ocean circulation models, includes advection by three–dimensional currents, turbulent mixing, radioactive decay and adsorption/release of radionuclides between water and bed sediments. Adsorption/release processes are described by means of a dynamic model based upon kinetic transfer coefficients. A stochastic method is used to solve turbulent mixing, decay and water/sediment interactions. The main results of these oceanic radionuclide transport studies are summarized in this paper. Particularly, the potential leakage of 137Cs from dumped nuclear wastes in the north Atlantic region was studied. Furthermore, hypothetical accidents, similar in magnitude to the Fukushima accident, were simulated for nuclear power plants located around the Indian Ocean coastlines. Finally, the transport of radionuclides resulting from the release of stored water, which was used to cool reactors after the Fukushima accident, was analyzed in the Pacific Ocean.