Drafts are sequential allocation procedures for distributing heterogeneous and indivisible objects among agents subject to some priority order (e.g., allocating players' contract rights to teams in professional sports leagues). Agents report ordinal preferences over objects and bundles are partially ordered by pairwise comparison. We provide three characterizations of draft rules. Firstly, they are the only allocation rules which are respectful of a priority (RP), envy-free up to one object (EF1), non-wasteful (NW) and resource-monotonic (RM). RP and EF1 are crucial for competitive balance in sports leagues. We also prove three related impossibility theorems: (i) weak strategy-proofness (WSP) is incompatible with RP, EF1, and NW; (ii) WSP is incompatible with EF1 and (Pareto) efficiency (EFF); and (iii) when there are two agents, strategy-proofness (SP) is incompatible with EF1 and NW. However, draft rules satisfy the competitive-balance properties, RP and EF1, together with EFF and maxmin strategy-proofness. If agents may declare some objects unacceptable, then draft rules are characterized by RP, EF1, NW, and RM, in conjunction with individual rationality and truncation-invariance. In a model with variable populations, draft rules are characterized by EF1, EFF, and RM, together with (population) consistency, top-object consistency, and neutrality.