We study the diversity-multiplexing tradeoff (DMT) for the full-duplex relay channel when the source and the destination have multiple antennas, and the relay has 1 or more. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), partial decode-and-forward (PDF), and compress-and-forward (CF) protocols. We study the effect of increased degrees of freedom in the direct link and the source-relay channel when multiple antennas are introduced. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it cannot maintain its good performance when the degrees of freedom in the direct link is increased. CF proves to be a more robust strategy, which works well in multi-antenna scenarios studied in this paper. We also extend our results for clustered relay networks to find DMT upper bounds and achievable performances.