Functional magnetic resonance imaging has become an invaluable tool for cognitive neuroscience, despite the fact that many of the physiological mechanisms giving rise to the effect are not well understood. We review the known biochemical and physiological basis of the technique and discuss how, within the noted limits, one might fully exploit the spatial and temporal resolution that is intrinsic to the very high magnetic fields that we use for human studies. This noninvasive brain mapping technique relies on the changes in blood oxygenation, blood volume, and blood flow, and we discuss some of the issues influencing the effects of these hemodynamic parameters on image intensity.