The successful design of sensor network architectures depends crucially on the structure of the sampling, observation, and communication processes. One of the most fundamental ques- tions concerns the sufficiency of discrete approximations in time, space, and amplitude. In the case of space and time, the question can be rephrased as whether there is a spatio- temporal sampling theorem for typical data sets in sensor net- works. This question has a positive answer in many cases of interest. The issue of discretization of amplitudes is more subtle and can be expressed as the question of whether there is a (source/channel) separation theorem for typical sensor networks. We show that this question has a negative answer in general and that the price of separation can be large. To illustrate these issues, we review the underlying theory and discuss specific examples.