RNA viruses are often thought of as possessing almost limitless adaptability as a result of their extreme mutation rates. However, high mutation rates also put a cap on the size of the viral genome by establishing an error threshold, beyond which lethal numbers of deleterious mutations accumulate. Herein, I argue that a lack of genomic space means that RNA viruses will be subject to important evolutionary constraints because specific sequences are required to encode multiple and often conflicting functions. Empirical evidence for these constraints, and how they limit viral adaptability, is now beginning to accumulate. Documenting the constraints to RNA virus evolution has important implications for predicting the emergence of new viruses and for improving therapeutic procedures.