We present a new framework for code-division multiple access (CDMA) communication over fast fading mobile wireless channels. The performance of the RAKE receiver, which is at the heart of existing CDMA systems, degrades substantially under fast fading encountered in many mobile scenarios. Due to the time-varying nature of the fast fading channel, we employ joint time-frequency processing, which is a powerful approach to time-varying signal processing. Whereas the RAKE receiver exploits multipath diversity to combat fading, our framework is based on joint multipath-Doppler diversity facilitated by a fundamental time-frequency decomposition of the channel into independent flat fading channels. Diversity processing is achieved by a time-frequency generalization of the RAKE receiver which can be leveraged into several important aspects of system design. Performance analysis shows that CDMA systems based on the time-frequency RAKE receiver, due to their inherently higher level of diversity, can potentially deliver significant performance gains over existing systems.