Antimicrobial resistance threatens a resurgence of life-threatening bacterial infections and the potential demise of many aspects of modern medicine. Despite intensive drug discovery efforts, no new classes of antibiotics have been developed into new medicines for decades, in large part owing to the stringent chemical, biological and pharmacological requisites for effective antibiotic drugs. Combinations of antibiotics and of antibiotics with non-antibiotic activity-enhancing compounds offer a productive strategy to address the widespread emergence of antibiotic-resistant strains. In this Review, we outline a theoretical and practical framework for the development of effective antibiotic combinations.