In this dissertation, we investigate the effects of having imperfect channel state information due to limited training and feedback resources in multi-user systems with multiple antennas. We find that while the achievable rate is highly sensitive to the quality of channel training and feedback, the rate gap relative to the rate achievable with perfect channel information can be uniformly bounded for all values of signal-to-noise ratio, with proper design of the feedback link to acquire accurate channel information, that is, the multiplexing gain can be preserved. Further, when a large number of users are present in a system, we find the strong requirement for accurate channel information remains, contrary to many transmission strategies that are commonly proposed for this regime. We conclude that given a limited feedback budget, it is desirable to first use resources to acquire highly accurate channel information, and only then allocate resources to exploit multi-user diversity. We also obtain results characterizing the statistics of random subspace quantization, which we use to compute the reduction in feedback overhead possible when this form of quantization is used. Finally, we consider open-loop multi-hop ad hoc networks with multiple antennas and opportunistic routing, and investigate using multiple antennas to optimize the spatial reuse, per-hop length and per-hop rate to maximize end-to-end performance.