Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean.The basic theoretical ideas for that have been borrowed from the phenomenon of chaotic advection in fluids,an analogue of dynamical Hamiltonian chaos in mechanics.The starting point for analysis is a velocity field obtained by this or that way.Being motivated by successful applications of that approach to simplified analytic models of geophysical fluid flows,researchers now work with satellite-derived velocity fields and outputs of sophisticated numerical models of ocean circulation.This review gives an introduction to some of the basic concepts and methods used to study chaotic mixing and transport in the ocean and a brief overview of recent results with some practical applications of Lagrangian tools to identify Lagrangian fronts favourable for fishing grounds and to monitor spreading of Fukushima-derived radionuclides in the ocean.