We discuss some recent results on adaptive modulation and coding for fading channels. The connection between these results and the corresponding Shannon capacity limits and optimal transmission strategies are also explored. We first describe our work on adaptive trellis and turbo-coded MQAM, for flat-fading channels, including the impact of channel estimation error and feedback delay. Next we consider frequency-selective fading channels. We show that multicarrier modulation with adaptive loading is optimal for finite block lengths. However, as the blocklength grows to infinity Shannon theory indicates that a forward/backward coding strategy is required. We discuss various methods to implement such an adaptive strategy and how the performance of these methods might differ from that of adaptive multicarrier modulation. Next we examine adaptive modulation techniques for simultaneous voice and data transmission. Specifically, we propose a simple transmission strategy that simultaneously meets the delay and BER requirements of voice while maximizing the data throughput. The connection between these results and previous results on outage (delay-limited) capacity are outlined, along with extensions of this technique to more general multimedia systems with different data rate, BER, and delay requirements. Finally, we discuss adaptive CDMA strategies for voice and data users in multiaccess fading channels.