Recent years have witnessed a revival of both industrial and academic interest in improving congestion control designs. The quest for better congestion control is complicated by the extreme diversity and range of (i) the design space (as exemplified by the stark conceptual and operational differences between recent proposals [2, 4, 6]), (ii) the desired properties (ranging from high performance to fairness to TCP-friendliness), (iii) the envisioned operational setting (inter- and intra-datacenter, wireless, the commercial Internet, satellite), and (iv) the application loads and requirements (small vs. large traffic demands, latency- vs. bandwidth-sensitive). Most congestion control research uses simulation and experiments under a limited range of network conditions. This is extremely important for understanding the detailed performance of particular schemes in specific settings, but provides limited insight into the more general properties of these schemes and no information about the inherent limits (such as, which properties are simultaneously achievable and which are mutually exclusive). In contrast, traditional theoretical approaches are typically focused on the design of protocols that achieve specific, predetermined objectives (e.g., network utility maximization [7]), or the analysis of specific protocols (e.g., from control-theoretic perspectives [12]), as opposed to exploring the inherent tensions/derivations between desired properties. We advocate an axiomatic approach to congestion control, which is complementary to the experimental and theoretical work currently being pursued. Our approach, modeled on similar efforts in social choice theory and game theory [1], identifies a set of requirements ("axioms") and then identifies (i) which of its subsets of requirements can coexist (i.e., there are designs that achieve all of them) and which subsets cannot be met simultaneously (i.e., no design can simultaneously achieve all of them), and (ii) whether some requirements immediately follow from satisfying other requirements. Thus, the axiomatic approach can shed light on the inherent tradeoffs involved in congestion control protocol design, and can be leveraged to classify existing and proposed solutions according to the properties they satisfy.