This paper develops the theory of both optimum and adaptive MIMO radar. It is shown that the optimum MIMO transmit-receiver pair consists of a coupled multidimensional eigensystem and whitening matched filter. Also introduced, is an design procedure for the clutter dominant case. After illustrating theoretical performance gains relative to conventional radar, we address the practical problem of adapting the transmit-receiver pair on-the-fly when the optimization must address multiple possible targets and/or signal (input) dependent noise (e.g., clutter). The resulting architecture combines the orthogonal transmit waveform MIMO radar with the aforementioned coupled transmit-receiver design pair with adaptive estimates for the radar channel.