This paper reviews radar architectures that employ multiple transmit and multiple receive channels to improve the performance of synthetic aperture radar (SAR) systems. These advanced architectures have been dubbed multiple-input multiple-output SAR (MIMO-SAR) in analogy to MIMO communication systems. Considerable confusion arose, however, with regard to the selection of suitable waveforms for the simultaneous transmission via multiple antennas. In this paper, it is shown that the mere use of orthogonal waveforms is insufficient for the desired performance improvement in view of most SAR applications. As a solution to this fundamental MIMO-SAR problem we had previously suggested to exploit the special data acquisition geometry of a side-looking imaging radar equipped with multiple receiver channels in addition to appropriately designed waveforms transmitted by multiple antennas. Here, we extend this approach to a more general set of radar waveforms with special correlation properties that satisfy a short-term shift-orthogonality condition. We show that the echoes from simultaneously transmitted pulses can be separated if the short-term shift orthogonality is combined with digital beamforming on receive in elevation. This enables the implementation of a fully functional MIMO-SAR without correlation noise leakage for extended scattering scenarios.