The complement system is a key innate immune defence against infection and an important driver of inflammation; however, these very properties can also cause harm. Inappropriate or uncontrolled activation of complement can cause local and/or systemic inflammation, tissue damage and disease. Complement provides numerous options for drug development as it is a proteolytic cascade that involves nine specific proteases, unique multimolecular activation and lytic complexes, an arsenal of natural inhibitors, and numerous receptors that bind to activation fragments. Drug design is facilitated by the increasingly detailed structural understanding of the molecules involved in the complement system. Only two anti-complement drugs are currently on the market, but many more are being developed for diseases that include infectious, inflammatory, degenerative, traumatic and neoplastic disorders. In this Review, we describe the history, current landscape and future directions for anti-complement therapies.