This paper reviews experimental and theoretical studies of the effects of heterogeneities in porous media on miscible and immiscible flow carried out in the Reservoir Physics Group at Imperial College over the past 20 years. Our aims have been to clearly define the physics of displacement flow. In our experiments we have used visual models with unconsolidated glass bead packs having carefully controlled permeability and wettability heterogeneities. The experiments provide visual evidence of the processes occurring within such heterogeneous porous media. For instance, miscible displacement experiments have shown that permeability heterogeneities within the reservoir will affect enhanced recovery schemes in either continuous injection or slug mode, due to viscous crossflow effects. The experimental evidence has been used to develop equations which predict the effects of viscous crossflow in layered systems and also enable design criteria for estimating slug volumes. We have also used our experimental results to validate the results obtained from numerical simulation. Immiscible displacement experiments have shown the large effects on residual saturation and recovery due to the presence of heterogeneities. During a waterflood, high permeability and oil-wet regions were by-passed due to capillary pressure differences, giving rise to high residual oil saturations in these regions. The major differences observed between miscible and immiscible displacements are due to saturation effects occurring during immiscible multi-phase flow, which manifest themselves in relative permeability and capillary pressure concepts, particularly at the boundaries. The miscible displacement studies have important implications for the planning of large scale reservoir  EOR processes, whereas the immiscible displacement studies are important for the correct interpretation of core data, and for the assessment of quantities and placement of residual oil.