With the increasing application of magnetic resonance imaging (MRI) and MR angiography in parenchymal liver disease, methods are becoming more widely available for noninvasive measurement of visceral blood flow. Amplitude-based (time-of-flight) and phase-based techniques have proved effective for measurement of portal blood flow, and phase-sensitive methods are applicable to arterial flow measurements. Because respiratory motion degrades the quality of examinations in the abdomen, it is desirable to use methods that can generate flow information in a breath-hold period. Although substantial technical difficulties persist for quantitative arterial flow measurements in the abdomen, the technical requirements for venous flow are less stringent, and important clinical information can be derived using straightforward techniques. The authors describe the principles of flow measurement using time-of-flight and phase methods in visceral arteries and veins, and discuss their practical implementation. Clinical applications are discussed, based on the experience of the authors and others working in the field.