Phase imaging benefits from strong susceptibility effects at very high field and the high signal-to-noise ratio (SNR) afforded by multi-channel coils. Combining the information from coils is not trivial, however, as the phase that originates in local field effects (the source of interesting contrast) is modified by the inhomogeneous sensitivity of each coil. This has historically been addressed by referencing individual coil sensitivities to that of a volume coil, but alternative approaches are required for ultra-high field systems in which no such coil is available. An additional challenge in phase imaging is that the phase that develops up to the echo time is " wrapped" into a range of 2p radians. Phase wraps need to be removed in order to reveal the underlying phase distribution of interest. Beginning with a coil combination using a homogeneous reference volume coil -the Roemer approach -which can be applied at 3 T and lower field strengths, we review alternative methods for combining single-echo and multi-echo phase images where no such reference coil is available. These are applied to high-resolution data acquired at 7 T and their effectiveness assessed via an index of agreement between phase values over channels and the contrast-to-noise ratio in combined images. The virtual receiver coil and COMPOSER approaches were both found to be computationally efficient and effective. The main features of spatial and temporal phase unwrapping methods are reviewed, placing particular emphasis on recent developments in temporal phase unwrapping and Laplacian approaches. The features and performance of these are illustrated in application to simulated and high-resolution in vivo data. Temporal unwrapping was the fastest of the methods tested and the Laplacian the most robust in images with low SNR. (C) 2016 The Authors. NMR in Biomedicine published by John Wiley & Sons Ltd.