Water/fat separation in the presence of B₀ field inhomogeneity is a problem of considerable practical importance in MRI. This article describes two complementary methods for estimating the water/fat images and the field inhomogeneity map from Dixon‐type acquisitions. One is based on variable projection (VARPRO) and the other on linear prediction (LP). The VARPRO method is very robust and can be used in low signal‐to‐noise ratio conditions because of its ability to achieve the maximum‐likelihood solution. The LP method is computationally more efficient, and is shown to perform well under moderate levels of noise and field inhomogeneity. These methods have been extended to handle multicoil acquisitions by jointly solving the estimation problem for all the coils. Both methods are analyzed and compared and results from several experiments are included to demonstrate their performance. Magn Reson Med 59:571–580, 2008. © 2008 Wiley‐Liss, Inc.