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Simultaneous multislice (SMS) acquisitions have recently received much attention as a means of increasing single-shot imaging speed. SMS acquisitions combine the advantages of single-shot sampling and acceleration along the slice dimension which was previously limited to three-dimensional (3D) volumetric acquisitions. A two-dimensional description of SMS sampling and reconstruction has become established in the literature. Here, we present a more general 3D Fourier encoding and reconstruction formalism for SMS acquisitions that can easily be applied to non-Cartesian SMS acquisitions.An “SMS 3D” k-space is defined in which the field of view along the slice select direction is equal to the number of excited slices times their separation. In this picture, SMS acceleration can be viewed as an undersampling of SMS 3D k-space that can be freely distributed between the in-plane and slice directions as both are effective phase-encoding directions.Use of the SMS 3D k-space picture is demonstrated in phantom and in vivo brain acquisitions including data obtained with blipped-controlled aliasing in parallel imaging sampling. SMS sensitivity encoding reconstruction is demonstrated as well as non-Cartesian SMS imaging using blipped spiral trajectories.The full framework of reconstruction methods can be applied to SMS acquisitions by employing a 3D k-space approach. The blipped-controlled aliasing in parallel imaging method can be viewed as a special case of undersampling an SMS 3D k-space. The extension of SMS methods to non-Cartesian 3D sampling and reconstruction is straightforward. Magn Reson Med 71:2071–2081, 2014. © 2013 Wiley Periodicals, Inc.