This paper provides an overview of the resource sharing networks introduced by Massoulié and Roberts [20] to model the dynamic behavior of Internet flows. Striving to separate the model class from the applications that motivated its development, we assume no prior knowledge of communication networks. The paper also presents an open problem, along with simulation results, a formal analysis, and a selective literature review that provide context and motivation. The open problem is to devise a policy for dynamic resource allocation that achieves what we call hierarchical greedy ideal (HGI) performance in the heavy traffic limit. The existence of such a policy is suggested by formal analysis of an approximating Brownian control problem, assuming that there is “local traffic” on each processing resource.