Fluid flow is introduced through the Navier-Stokes equations. This is solved for flow in a cylindrical tube, while approximate solutions are presented for two-phase flow with one phase confined to a wetting or pinned layer in the corners of the pore space. Darcy’s law is presented as the macroscopic counter-part to the Navier-Stokes equations for low Reynolds number flow. Permeability and the Leverett J function are introduced and examples are presented, relating measured values to typical pore sizes. The multiphase Darcy law is presented with a definition of relative permeability. The approximations in this formulation are explored in detail with an analysis of pore-scale dynamics, correlation lengths, energy balance and ganglion mobilization as a function of capillary number, or the ratio of viscous to capillary forces. Numerical methods to solve for single and multiphase flow are reviewed. Direct simulation on pore-space images cannot alone provide reliable macroscopic properties for complex rocks. The use of a network model as an upscaling tool is discussed. Last, putative extensions to the multiphase Darcy law are presented, together with flow regimes as a function of capillary number, contact angle, viscosity ratio and heterogeneity.