The complement system is a major component of the innate immune system that recognizes invading pathogens and eliminates them by means of an array of effector mechanisms, in addition to using direct lytic destruction. Viruses, in spite of their small size and simple composition, are also deftly recognized and neutralized by the complement system. In turn, as a result of years of coevolution with the host, viruses have developed multiple mechanisms to evade the host complement. These complex interactions between the complement system and viruses have been an area of focus for over three decades. In this article, we provide a broad overview of the field using key examples and up-to-date information on the complement-evasion strategies of viruses.