Wireless Sensor Networks (WSNs), where a multiplicity of sensors observe a physical phenomenon and transmit their measurements to one or more sinks, pertain to the class of multi-terminal source and channel coding problems of Information Theory. In this category, "real-time" coding is often encountered for WSNs, referring to the problem of finding the minimum distortion (according to a given measure), under transmission power constraints, attainable by encoding and decoding functions, with stringent limits on delay and complexity. On the other hand, the Decision Theory approach seeks to determine the optimal coding/decoding strategies or some of their structural properties. Since encoder(s) and decoder(s) possess different information, though sharing a common goal, the setting here is that of Team Decision Theory. A more pragmatic vision rooted in Signal Processing consists of fixing the form of the coding strategies (e.g., to linear functions) and, consequently, finding the corresponding optimal decoding strategies and the achievable distortion, generally by applying parametric optimization techniques. All approaches have a long history of past investigations and recent results. The goal of the present paper is to provide the taxonomy of the various formulations, a survey of the vast related literature, examples from the authors' own research, and some highlights on the inter-play of the different theories.