Reproduction of RNA viruses is typically error-prone due to the infidelity of their replicative machinery and the usual lack of proofreading mechanisms. The error rates may be close to those that kill the virus. Consequently, populations of RNA viruses are represented by heterogeneous sets of genomes with various levels of fitness. This is especially consequential when viruses encounter various bottlenecks and new infections are initiated by a single or few deviating genomes. Nevertheless, RNA viruses are able to maintain their identity by conservation of major functional elements. This conservatism stems from genetic robustness or mutational tolerance, which is largely due to the functional degeneracy of many protein and RNA elements as well as to negative selection. Another relevant mechanism is the capacity to restore fitness after genetic damages, also based on replicative infidelity. Conversely, error-prone replication is a major tool that ensures viral evolvability. The potential for changes in debilitated genomes is much higher in small populations, because in the absence of stronger competitors low-fit genomes have a choice of various trajectories to wander along fitness landscapes. Thus, low-fit populations are inherently unstable, and it may be said that to run ahead it is useful to stumble. In this report, focusing on picornaviruses and also considering data from other RNA viruses, we review the biological relevance and mechanisms of various alterations of viral RNA genomes as well as pathways and mechanisms of rehabilitation after loss of fitness. The relationships among mutational robustness, resilience, and evolvability of viral RNA genomes are discussed. © 2018 American Society for Microbiology. All Rights Reserved.