Several methods are now available for measuring cerebral perfusion and related hemodynamic parameters using magnetic resonance imaging (MRI). One class of techniques utilizes electromagnetically labeled arterial blood water as a noninvasive diffusible tracer for blood flow measurements. The electromagnetically labeled tracer has a decay rate of T1, which is sufficiently long to allow perfusion of the tissue and microvasculature to be detected. Alternatively, electromagnetic arterial spin labeling (ASL) may be used to obtain qualitative perfusion contrast for detecting changes in blood flow, similar to the use of susceptibility contrast in blood oxygenation level dependent functional MRI (BOLD fMRI) to detect functional activation in the brain. The ability to obtain blood flow maps using a non-invasive and widely available modality such as MRI should greatly enhance the utility of blood flow measurement as a means of gaining further insight into the broad range of hemodynamically related physiology and pathophysiology. This article describes the biophysical considerations pertaining to the generation of quantitative blood flow maps using a particular form of ASL in which arterial blood water is continuously labeled, termed continuous arterial spin labeling (CASL). Technical advances permit multislice perfusion imaging using CASL with reduced sensitivity to motion and transit time effects. Interpretable cerebral perfusion images can now be reliably obtained in a variety of clinical settings including acute stroke, chronic cerebrovascular disease, degenerative diseases and epilepsy. Over the past several years, the technical and theoretical foundations of CASL perfusion MRI techniques have evolved from feasibility studies into practical usage. Currently existing methodologies are sufficient to make reliable and clinically relevant observations which complement structural assessment using MRI. Future technical improvements should further reduce the acquisition times for CASL perfusion MRI, while increasing the slice coverage, resolution and stability of the images. These techniques have a broad range of potential applications in clinical and basic research of brain physiology, as well as in other organs.