After a decade of evolution and application of diffusion imaging, a large body of literature has been accumulated. It is in this context that the accuracy and precision of diffusion‐weighted and quantitative diffusion MRI are reviewed. The emphasis of the review is on practical methods for clinical human imaging, particularly in the brain. The requirements for accuracy and precision are reviewed for various clinical and basic science applications. The methods of measuring and calculating diffusion effects with MRI are reviewed. The pulse gradient spin echo (PGSE) methods are emphasized as these methods are used most commonly in the clinical setting. Processing of PGSE data is reviewed. Various PGSE encoding schemes are also reviewed in terms of the accuracy and precision of isotropic and anisotropic diffusion measurements. The broad range of factors impacting the accuracy of the PGSE methods and other encoding schemes is then considered. Firstly, system inaccuracies such as background imaging gradients, gradient linearity, refocusing RF pulses, eddy currents, image misregistration, noise and dynamic range are considered. A second class of inaccuracies is contributed by the bulk effects of the imaged object, and include sample background gradients, subject motion of cerebrospinal fluid and organs, and aperiodic organ motion. A final category of potential inaccuracies is classified as being contributed by microscopic, biophysical tissue properties and include partial volume effects, anisotropy, restriction, diffusion distance, compartmentation, exchange, multiexponential diffusion decay, T2 weighting and microvascular perfusion. Finally, the application of diffusion methods to studies of blood flow in the microvasculature (i.e. the arterioles, capillaries and venules) are reviewed in detail, particularly in terms of feasibility and the stringent accuracy and precision requirements. Recent provocative studies examining the use of PGSE approaches to suppress microvascular signals in brain functional MRI (fMRI) are also reviewed.