Adaptive transmission systems improve the throughput of wireless communication systems by utilizing some knowledge of the channel state to adapt or allocate transmitter resources. This dissertation investigates the acquisition of channel state information for adaptive transmission systems. Departing from the common assumption that the feedback channel is error free, we model the feedback channel as a practical wireless channel with fading and additive noise attributes. We show that feedback errors could significantly reduce the gains promised by adaptive transmission. Subsequently, we propose feedback receivers that exploit some knowledge of the channel statistics to mitigate the performance degradation caused by the feedback channel. This work is extended to multiuser systems, where new problems are investigated, namely, quantization errors coupled with feedback errors, and multi-access interference. system. Finally, we consider CSI acquisition for transmit antenna selection and discuss the tradeoffs between capacity gain and training. A reduced complexity suboptimal search algorithm is also developed using the channel's temporal correlation.