This review focuses on the experimental data showing the abundance of structural disorder within the nucleoprotein (N) and phosphoprotein (P) from three paramyxoviruses, namely Nipah (NiV), Hendra (HeV) and measles (MeV) viruses. We provide a detailed description of the molecular mechanisms governing the disorder-to-order transition of the intrinsically disordered C-terminal domains (N(TAIL)) of their N proteins upon binding to the C-terminal X domain (XD) of the homologous P proteins. We also show that a significant flexibility persists within N(TAIL)-XD complexes, which therefore provide illustrative examples of "fuzziness". 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. 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.