The successful design of sensor network architectures depends crucially on the structure of the sampling, observation, and communication processes. One of the most fundamental questions concerns the sufficiency of discrete approximations in time, space, and amplitude. More explicitly, to capture the spatiotemporal variations of the underlying signals, when is it sufficient to build sensor network systems that work with discrete-time and -space representations? And can the underlying amplitude varia- tions of interest be observed at the highest possible fidelity if the sensors quantize their obser- vations, assuming that quantization is done in the most sophisticated fashion, exploiting the principles of (ideal) distributed source coding? The former can be rephrased as the question of whether there is a spatiotemporal sampling theorem for typical data sets in sensor networks. This question has a positive answer in many cases of interest, based on the physics of the processes to be observed. The latter can be expressed as the question of whether there is a (source/channel) separation theorem for typical sensor network scenarios. We show that this question has in many cases a nega- tive answer, and we show that the price of separation can be large. To illustrate the conceptual issues related to sampling, source representation/coding and communication in sensor networks, we review the underlying theory and discuss specific examples.