In this paper, we introduce the Theory of Bottleneck Ordering, a mathematical framework that reveals the bottleneck structure of data networks. This theoretical framework provides insights into the inherent topological properties of a network at least in three areas: (1) It identifies the regions of influence of each bottleneck; (2) it reveals the order in which bottlenecks (and flows traversing them) converge to their steady state transmission rates in distributed congestion control algorithms; and (3) it provides key insights to the design of optimized traffic engineering policies. We demonstrate the efficacy of the proposed theory in TCP congestion-controlled networks for two broad classes of algorithms: congestion-based algorithms (BBR) and loss-based additive-increase/multiplicative-decrease algorithms (Cubic and Reno). Among other results, our network experiments show that: (1) Qualitatively, both classes of congestion control algorithms behave as predicted by the bottleneck structure of the network; (2) flows compete for bandwidth only with other flows operating at the same bottleneck level; (3) BBR flows achieve higher performance and fairness than Cubic and Reno flows due to their ability to operate at the right bottleneck level; (4) the bottleneck structure of a network is ever-changing and its levels can be folded due to variations in the flows’ round trip times; and (5) against conventional wisdom, low-hitter flows can have a large impact to the overall performance of a network.