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We review the recently developed dynamical systems and chaos theory approach in oceanography that focuses on finding and specifying fundamental geometric structures in the ocean and their impact on large-scale transport and mixing of water masses. It is demonstrated that the methods of that theory in the framework of the Lagrangian approach work well with both kinematic and dynamic models and with real velocity fields derived from satellite altimeter measurements of anomalies of the sea height. We start with simple models of the eddy and jet flows and show how some underlying geometric structures arise and produce chaotic advection of passive particles even in time-periodic flows. Then we apply the Lagrangian methods for detecting Lagrangian fronts with favorable fishery conditions in the North Pacific Ocean and for modelling radionuclide propagation from the Fukushima–Daiichi nuclear plant. Finally, we discuss the perspectives on the Lagrangian approach in oceanography and its possible practical applications.

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