Measurement of regional cerebral blood volume and flow in vivo has proved useful in the study of normal and diseased states in the brain. This circumstance has led to a variety of techniques for quantitative determination and has continued to motivate the search for ever safer and more accurate methods of measurement. New advances in fast MR imaging provided data potentially amenable to analysis by tracer-kinetic methods. In this way, dynamic susceptibility contrast MR imaging during the first pass of an injected tracer has been used to quantitatively assess cerebral perfusion. However, the use of time-concentration data to calculate blood flow (CBF), vascular volume (CBV) and tracer mean transit time (MTT) is not straightforward because these data reflect not only the vascular physiology of the tissue, but also the input function, which is the concentration of the tracer when it enters the region of interest. In this paper we have demonstrated the indicator (tracer) dilution principle, which provides a mathematical basis for characterizing the vascular physiology of a tissue measured by the changes in concentration of a tracer within the tissue as a function of time. We have shown the necessity to put forward some assumptions about the nature of the vascular bed and the importance of the arterial input function to describe the tissue pulse response function accurately. We have described different parametrical and non–parametrical deconvolution approaches which allowed us to determine relative and absolute values of hemodynamic parameters such as CBV, CBF and MTT. Finally, after reviewing the entire of MR cerebral perfusion literature, our claim is that no ideal method is currently available to quantify MR cerebral perfusion.