Hybrid multiple-antenna transceivers, which combine large-dimensional analog pre/postprocessing with lower-dimensional digital processing, are the most promising approach for reducing the hardware cost and training overhead in massive MIMO systems. This article provides a comprehensive survey of the various incarnations of such structures that have been proposed in the literature. We provide a taxonomy in terms of the required channel state information, that is, whether the processing adapts to the instantaneous or average (second-order) channel state information; while the former provides somewhat better signal- to-noise and interference ratio, the latter has much lower overhead for CSI acquisition. We furthermore distinguish hardware structures of different complexities. Finally, we point out the special design aspects for operation at millimeter-wave frequencies.