We herein review available computational and experimental data pointing to the abundance of structural disorder within the nucleoprotein (N) and phosphoprotein (P) from three paramyxoviruses, namely the measles (MeV), Nipah (NiV) and Hendra (HeV) viruses. We provide a detailed molecular description of the mechanisms governing the disorder-to-order transition that the intrinsically disordered C-terminal domain (NTAIL) of their N proteins undergoes upon binding to the C-terminal X domain (PXD) of the homologous P proteins. We also show that NTAIL–PXD complexes are “fuzzy”, i.e., they possess a significant residual disorder, and discuss the possible functional significance of this fuzziness. Finally, we emphasize the relevance of N–P interactions involving intrinsically disordered proteins as promising targets for new antiviral approaches, and end up summarizing the general functional advantages of disorder for viruses.