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Relay networks was formulated in the 1970s, but the complete characterization of the achievable rates of relay networks is open, even for the simplest three node network (single source, single destination, one relay). This is true even for the special case of Gaussian relay networks, where Gaussian broadcast and multiple access channels model the relay network interactions. Our philosophy was to simplify the models and obtain insights with the hope to approximately characterize the general Gaussian relay network capacity. We started with a linear deterministic model which incorporated both the main distinguishing characteristics of wireless channels, i.e., broadcast and multiple access. For such a model we had a complete characterization of the relay network capacity in terms of an intuitively satisfying max-flow min-cut result . This also led to an achievability result for arbitrary deterministic model determining the relay network interactions (broadcast, multiple access). The analysis for arbitrary deterministic functions needed the notion of typicality and gave insight to an approximate characterization of the wireless relay network capacity.