Typical diffusion measurements use Stejskal-Tanner pulsed gradient spin echo sequences to provide information about the average diffusion and displacement profiles of particles in a sample. To derive structural information, a measured displacement profile has to be related by means of a model to the physical and geometrical properties of the tissue, such as diffusion coefficients and shapes of semi-permeable membranes of compartments in the system. The behavior of the NMR signal and the measured ADC are greatly affected by the cellular architecture of a tissue, mainly because cellular membranes are relatively impermeable to water. For long diffusion times, and small signal attenuations, ADC is relatively insensitive to how it is measured. In general, however, ADC values are not readily interpreted unless the measuring conditions are specified in detail. For given measuring conditions, ADC depends on intra- and extracellular diffusion coefficients, membrane permeabilities, cell sizes and the cellular volume fraction. If intra- and extracellular T2 relaxation rates are different enough, ADC may also depend on the relaxation properties of the system and the echo time. An improved understanding of the precise influence of these factors has been obtained by detailed consideration of theoretical and computer models that can be related to experimental data in simple systems. Further refinements of such models should advance our understanding of water diffusion in tissues.