This chapter first introduces CS in the conventional setting where one device acquires one signal and sends it to a receiver, and then extends it to the distributed framework in which multiple devices acquire multiple signals. In particular, we focus on two key problems related to the distributed setting. The former is the definition of sparsity models for an ensemble of signals, as opposed to just one signal. The second is the structure of the corresponding recovery algorithm, which can be centralized or distributed; each solution entails specific advantages and drawbacks that are preliminarily discussed in this chapter, whereas a detailed description of the corresponding recovery algorithms is given in Chaps. 4 and 5.