Ebola viruses and Marburg viruses, members of the filovirus family, are zoonotic pathogens that cause severe disease in people, as highlighted by the latest Ebola virus epidemic in West Africa. Filovirus disease is characterized by uncontrolled virus replication and the activation of host responses that contribute to pathogenesis. Underlying these phenomena is the potent suppression of host innate antiviral responses, particularly the type I interferon response, by viral proteins, which allows high levels of viral replication. In this Review, we describe the mechanisms used by filoviruses to block host innate immunity and discuss the links between immune evasion and filovirus pathogenesis.