There is great interest in the research community supporting the use of multiple antennas at the transmitter and receiver of a wireless link. Such systems can support the ever-growing demand for capacity and data services. Multiple antenna systems can effectively meet these demands by supporting higher data rates and/or providing increased channel reliability.Optimizing the downlink transmission of a multiple antenna system requires the availability of channel information at the transmitter. This information can be used to customize the transmitted waveform to the channel using appropriate precoding. This thesis furthers the development of multiple antenna precoding by designing feedback schemes that support their use. Existing feedback schemes place restrictions that limit the inherent flexibility of multiple antenna systems. This thesis develops practical, flexible and efficient feedback schemes for both the single and multiuser case.