Interest in the manner in which brain tissue signal decays with b factor in diffusion imaging schemes has grown in recent years following the observation that the decay curves depart from purely monoexponential decay behavior. Regardless of the model or fitting function proposed for characterizing sufficiently sampled decay curves (vide infra), the departure from monoexponentiality spells increased tissue characterization potential. The degree to which this potential can be harnessed to improve specificity, sensitivity and spatial localization of diseases in brain, and other tissues, largely remains to be explored. Furthermore, the degree to which currently popular diffusion tensor imaging methods, including visually impressive white matter fiber "tractography" results, have almost completely ignored the nonmonoexponential nature of the basic signal decay with b factor is worthy of communal introspection. Here we limit our attention to a review of the basic experimental features associated with brain water signal diffusion decay curves as measured over extended b-factor ranges, the simple few parameter fitting functions that have been proposed to characterize these decays and the more involved models, e.g.,"ruminations," which have been proposed to account for the nonmonoexponentiality to date.