Many protein functions can be traced to linear sequence motifs of less than five residues, which are often found within intrinsically disordered domains. In spite of their prevalence, their role in protein evolution is only beginning to be understood. The study of papillomaviruses has provided many insights on the evolution of protein structure and function. We have chosen the papillomavirus E7 oncoprotein as a model system for the evolution of functional linear motifs. The multiple functions of E7 proteins from paradigmatic papillomavirus types can be explained to a large extent in terms of five linear motifs within the intrinsically disordered N-terminal domain and two linear motifs within the globular homodimeric C-terminal domain. We examined the motif inventory of E7 proteins from over 200 known papillomavirus types and found that the motifs reported for paradigmatic papillomavirus types are absent from many uncharacterized E7 proteins. Several motif pairs occur more often than expected, suggesting that linear motifs may evolve and function in a cooperative manner. The E7 linear motifs have appeared or disappeared multiple times during papillomavirus evolution, confirming the evolutionary plasticity of short functional sequences. Four of the motifs appeared several times during papillomavirus evolution, providing direct evidence for convergent evolution. Interestingly, the evolution pattern of a motif is independent of its location in a globular or disordered domain. The correlation between the presence of some motifs and virus host specificity and tissue tropism suggests that linear motifs play a role in the adaptive evolution of papillomaviruses.