Even as the clinical impact of drug combinations continues to accelerate, no consensus on how to quantify drug synergy has emerged. Rather, surveying the landscape of drug synergy reveals the persistence of historical fissures regarding the appropriate domains of conflicting synergy models – fissures impacting all aspects of combination therapy discovery and deployment. Herein we chronicle the impact of these divisions on: (i) the design, interpretation, and reproducibility of high-throughput combination screens; (ii) the performance of algorithms to predict synergistic mixtures; and (iii) the search for higher-order synergistic interactions. Further progress in each of these subfields hinges on reaching a consensus regarding the long-standing rifts in the field.