The suppression of signal from fat constitutes a basic requirement in many applications of magnetic resonance imaging. To date, this is predominantly achieved during data acquisition, using fat saturation, inversion recovery, or water excitation methods. Postponing the separation of signal from water and fat until image reconstruction holds the promise of resolving some of the problems associated with these methods, such as failure in the presence of field inhomogeneities or contrast agents. In this article, methods are reviewed that rely on the difference in chemical shift between the hydrogen atoms in water and fat to perform such a retrospective separation. The basic principle underlying these so-called Dixon methods is introduced, and some fundamental implementations of the required chemical shift encoding in the acquisition and the subsequent water-fat separation in the reconstruction are described. Practical issues, such as the selection of key parameters and the appearance of typical artifacts, are illustrated, and a broad range of applications is demonstrated, including abdominal, cardiovascular, and musculoskeletal imaging. Finally, advantages and disadvantages of these Dixon methods are summarized, and emerging opportunities arising from the availability of information on the amount and distribution of fat are discussed.