A wide variety of fat suppression and water–fat separation methods are used to suppress fat signal and improve visualization of abnormalities. This article reviews the most commonly used techniques for fat suppression and fat–water imaging including 1) chemically selective fat suppression pulses “FAT-SAT”; 2) spatial-spectral pulses (water excitation); 3) short inversion time (TI) inversion recovery (STIR) imaging; 4) chemical shift based water–fat separation methods; and finally 5) fat suppression and balanced steady-state free precession (SSFP) sequences. The basic physical background of these techniques including their specific advantages and disadvantages is given and related to clinical applications. This enables the reader to understand the reasons why some fat suppression methods work better than others in specific clinical settings. J. Magn. Reson. Imaging 2010;31:4–18. © 2009 Wiley-Liss, Inc.