A wireless body area network (WBAN) enables real-time monitoring of physiological signals and helps with the early detection of life-threatening diseases. WBAN nodes can be located on, inside, or in close proximity to the body in order to detect vital signals. Measurements from sensors are processed and transmitted over wireless channels. Issues in sensing, signal processing, and communication have to be addressed before WBAN can be implemented. In this paper, we survey recent advances in research on signal processing for the sensor measurements, and we describe aspects of communication based on IEEE 802.15.6. We also discuss state-of-the-art WBAN channel modeling in all the frequencies specified by IEEE 802.15.6 as well as the need for new channel models for new different frequencies.