In this paper, we investigate properties of good coding strategies for a class of wireless sensor networks that could be termed "monitoring" networks: Their task is to monitor an underlying physical reality at the highest possible fidelity. Since the sensed signals are often analog, and the communication channels noisy, it will not generally be possible to exactly communicate the sensed signals. Rather, such sensor network scenarios involve both a compression and a communication problem. It is well known that these two tasks must be addressed jointly for optimal performance, but optimal performance is unknown in general.