Magnetic resonance imaging (MRI) is one of the most important diagnostic tools of modern healthcare. The signal in medical MRI predominantly originates from water and fat molecules. Separation of the two components into water-only and fat-only images can improve diagnosis, and is the premier non-invasive method for measuring the amount and distribution of fatty tissue. Fat-water imaging (FWI) enables fast fat/water separation by model-based estimation from chemical shift encoded data, such as multi-echo acquisitions. Qualitative FWI is sufficient for visual separation of the components, while quantitative FWI also offers reliable estimates of the fat percentage in each pixel. The major problems of current FWI methods are long acquisition times, long reconstruction times, and reconstruction errors that degrade image quality. In this thesis, existing FWI methods were reviewed, and novel fully automatic methods were developed and evaluated, with a focus on fast 3D image reconstruction. All MRI data was acquired on standard clinical scanners. A triple-echo qualitative FWI method was developed for the specific application of 3D whole-body imaging. The method was compared with two reference methods, and demonstrated superior image quality when evaluated in 39 volunteers. The problem of qualitative FWI by dual-echo data with unconstrained echo times was solved, allowing faster and more flexible image acquisition than conventional FWI. Feasibility of the method was demonstrated in three volunteers and the noise performance was evaluated. Further, a quantitative multi-echo FWI method was developed. The signal separation was based on discrete whole-image optimization. Fast 3D image reconstruction with few reconstruction errors was demonstrated by abdominal imaging of ten volunteers. Lastly, a method was proposed for quantitative mapping of average fatty acid chain length and degree of saturation. The method was validated by imaging different oils, using gas-liquid chromatography (GLC) as the reference. The degree of saturation agreed well with GLC, and feasibility of the method was demonstrated in the thigh of a volunteer. The developed methods have applications in clinical settings, and are already being used in several research projects, including studies of obesity, dietary intervention, and the metabolic syndrome.