Three-dimensional structural magnetic resonance imaging (MRI) and MRI velocimetry have been used to fully characterise the structure of the interparticle pore space and the single-phase Row held in a packed bed of alumina catalyst particles. Three orthogonal components of the velocity (V-x, V-y and V-g) are acquired such that the fluid velocity vector is determined at a pore-scale resolution of 156 mum The pore space has been analysed by unambiguously partitioning the pore space into individual poles. Characteristics of the individual pores are combined with the MRI velocity data to determine quantitative statistical information concerning Row through these pores. The ability of the lattice-Boltzmann simulation technique to predict the flow field visualised by MRI is also demonstrated by performing the simulation on a lattice derived directly from the MRI experimental three-dimensional image of the structure of the packed bed. A direct comparison of the MRI and lattice-Boltzmann results shows there is good agreement between the two methods. Using the pore analysis in conjunction with the velocity information, the flow field through the pore space is shown to be highly heterogeneous with 40% of the fluid Rowing through only 10% of the pores. We also show that the lattice-Boltzmann data may be used to calculate average molecular displacement propagators similar to those acquired experimentally for such systems. The effect of the wall on the fluid velocity and porosity is calculated as a function of distance from the wall. Some difference between the MRI and lattice-Boltzmann results are observed close to the wall because of inertial effects in the high velocity channels which are not simulated by the lattice-Boltzmann method. Finally, we present initial results from the extension of this work to two-phase flow in packed beds. A case study of the visualisation of the extent of wetting of the packing as a function of time following start-up is presented.