RNA viruses face dynamic environments and are masters at adaptation. During their short 'lifespans', they must surmount multiple physical, anatomical and immunological challenges. Central to their adaptative capacity is the enormous genetic diversity that characterizes RNA virus populations. Although genetic diversity increases the rate of adaptive evolution, low replication fidelity can present a risk because excess mutations can lead to population extinction. In this Review, we discuss the strategies used by RNA viruses to deal with the increased mutational load and consider how this mutational robustness might influence viral evolution and pathogenesis.