Research in chemical engineering is inherently challenging because of the need to describe the unsteady-state behaviour of multi-phase, multi-component systems. Therefore there has been long-standing interest in developing tomographic techniques which can be applied to 'look inside' chemical engineering systems and characterise hydrodynamics and chemical composition. This paper summarizes the `state-of-the-art' in ultra-fast magnetic resonance imaging applied to characterising hydrodynamics in single- and multi-phase flows. Typically 'ultra-fast' data acquisition implies acquisition of a 2-D data array of 128 x 128 pixels in less than 1 s. We report recent results showing the application of MR to characterize flows in such diverse systems as immiscible liquid flow in microchannels, gas-liquid pipe flow, granular dynamics in gas-fluidized beds and two-phase flow hydrodynamics in fixed-bed reactors.