While most people have an intuitive notion of “fairness” in allocating resources, it is difficult to quantify this intuition in a mathematical fairness function. Mathematical characterizations of fairness are particularly under-explored when users share multiple types of resources and combine the resources in different proportions. Yet such multi-resource allocations often arise in e-commerce settings, e.g., cloud platforms processing computational jobs with heterogeneous requirements for CPU, memory, network, bandwidth, etc. We develop a unifying framework for multi-resource fairness that generalizes single-resource fairness measures to address heterogeneity in user resource requirements and the resulting tradeoff between fairness and efficiency. We introduce two families of fairness functions that provide different fairness-efficiency tradeoffs, characterize the effect of user heterogeneity, and prove conditions under which these fairness functions satisfy the Pareto efficiency, sharing incentive, and envy-free properties. We then show that, under specific conditions on users’ resource requirements, a fairness-efficiency tradeoff need not exist. We finally show that these functions can be mapped to some intuitive fairness perceptions by examining the results of an informal online survey of users’ allocation preferences.