Diffusion-weighted MRI (DW-MRI) is a functional imaging technique that displays information about the extent and direction of random water motion in tissues. Water movement in tissues is modified by interactions with hydrophobic cellular membranes, intracellular organelles and macromolecules. DW-MRI provides information on extracellular-space tortuosity, tissue cellularity and the integrity of cellular membranes. Images can be sensitive to large or small displacements of water, therefore, macroscopic water flows and microscopic water displacements in the extracellular space can be depicted. Preclinical and clinical data indicate a number of potential roles of DW-MRI in the characterization of malignancy, including determination of lesion aggressiveness and monitoring response to therapy. This Review outlines the biological basis of observations made on DW-MRI and describes how measurements are acquired and quantified, and discusses the interpretation of images and limitations of the technique. The strength of evidence for adoption of DW-MRI as a biomarker for the assessment of tumor response is presented.