The two major transport processes occurring in the human body are diffusion and flow. When a rephased gradient–time profile is applied, both processes leave their fingerprint in the magnetic resonance signal. Plug flow along a single direction results in an additional signal phase, but stationary and non-stationary random flow leave the same fingerprint as diffusion – a signal attenuation. A classic approach to separate diffusion and non-plug flow is to use the difference in transport distance. It differs by more than an order of magnitude for typical time scales in MRI experiments and entails a much faster signal decay for the flow compartment than for the diffusion compartment. Besides the classical approach, further strategies have been proposed to reveal the nature of the flow processes in more depth by adding additional measurement dimensions to the experiment. These dimensions include inversion time, echo time, and field strength to alter the signal contributions, but duration and shape of the gradient-time profile were also employed to change the degree of flow-weighting and to probe flow correlation times. It was found that flow-compensated gradients strongly suppress the flow-related signal decay in vivo, indicating that a ballistic description is more appropriate than assuming a diffusion-like flow.