We review several methods that have been developed to infer microstructural and physiological information about isotropic and anisotropic tissues from diffusion weighted images (DWIs). These include Diffusion Imaging (DI), Diffusion Tensor Imaging (DTI), isotropically weighted imaging, and q-space imaging. Just as DI provides useful information about molecular displacements in one dimension with which to characterize diffusion in isotropic tissues, DTI provides information about molecular displacements in three dimensions needed to characterize diffusion is anisotropic tissues. DTI also furnishes scalar parameters that behave like quantitative histological or physiological 'stains' for different features of diffusion. These include Trace(D), which is related to the mean diffusivity, and a family of parameters derived from the diffusion tensor, D, which characterize different features of anisotropic diffusion. Simple thought experiments and geometrical constructs, such as the diffusion ellipsoid, can be used to understand water diffusion in isotropic and anisotropic media, and the NMR experiments used to characterize it.