Transport phenomena are studied in a large variety of dynamical systems with applications ranging from the analysis of fluid flow in the ocean and the predator-prey interaction in jellyfish to the investigation of blood flow in the cardiovascular system. Our approach to analyze transport is based on the methodology of so-called transfer operators associated with a dynamical system since this is particularly suitable. We describe the approach and illustrate it by two real world applications: the computation of transport for asteroids in the solar system and the approximation of macroscopic structures in the Southern Ocean.