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One of the advantages of arterial spin labeling (ASL) techniques over other techniques for measuring cerebral perfusion is that with ASL it is possible to achieve accurate quantification. This is particularly useful in the field of functional imaging, where accurate measurements of perfusion change can help untangle the complex physiological changes that occur following neuronal activation. However, the linearity of the perfusion estimate over a wide range of perfusion values may be more important than absolute values. For several years, single-compartment models have dominated the literature, and it has been assumed that the labeled water diffuses freely throughout the tissue voxel. However, recent work, as summarized in this review, has shown that this assumption is inaccurate and leads to an overestimation of perfusion at low perfusion rates, and an underestimation at high rates. The inclusion of restricted permeability of the capillary wall to water in a two-compartment model offers improved quantification. J. Magn. Reson. Imaging 2005. © 2005 Wiley-Liss, Inc.