In this review, we summarize the main experimental data showing the abundance of structural disorder within the measles virus (MeV) nucleoprotein (N) and phosphoprotein (P), and focus on the molecular mechanisms governing the disorder-to-order transition of the intrinsically disordered C-terminal domain of MeV N (N(TAIL)) upon binding to the C-terminal X domain of P (XD). The functional implications of structural disorder are discussed in light of the ability of disordered regions to establish a complex molecular partnership, thereby leading to a variety of biological effects, including tethering of the polymerase complex onto the nucleocapsid template, stimulation of viral transcription and replication, and virus assembly. We also discuss the ability of N(TAIL) to establish interactions with additional cellular co-factors, including the major inducible heat shock protein, which can modulate the strength of the N(TAIL)-XD interaction. Taking into account the promiscuity that typifies disordered regions, we propose that the main functional advantage of the abundance of disorder within viruses would reside in pleiotropy and genetic compaction, where a single gene would encode a single (regulatory) protein product able to establish multiple interactions via its disordered regions, and hence to exert multiple concomitant biological effects.