Measles, Nipah and Hendra viruses are severe human pathogens within the Paramyxoviridae family. Their non-segmented, single-stranded, negative-sense RNA genome is encapsidated by the nucleoprotein (N) within a helical nucleocapsid that is the substrate used by the viral RNA-dependent-RNA-polymerase (RpRd) for transcription and replication. The RpRd is a complex made of the large protein (L) and of the phosphoprotein (P), the latter serving as an obligate polymerase cofactor and as a chaperon for N. Both the N and P proteins are enriched in intrinsically disordered regions (IDRs), i.e. regions devoid of stable secondary and tertiary structure. N possesses a C-terminal IDR (NTAIL), while P consists of a large, intrinsically disordered N-terminal domain (NTD) and a C-terminal domain (CTD) encompassing alternating disordered and ordered regions. The V and W proteins, two non-structural proteins that are encoded by the P gene via a mechanism of co-transcriptional edition of the P mRNA, are prevalently disordered too, sharing with P the disordered NTD. They are key players in the evasion of the host antiviral response and were shown to phase separate and to form amyloid-like fibrils in vitro. In this review, we summarize the available information on IDRs within the N, P, V and W proteins from these three model paramyxoviruses and describe their molecular partnership. We discuss the functional benefit of disorder to virus replication in light of the critical role of IDRs in affording promiscuity, multifunctionality, fine regulation of interaction strength, scaffolding functions and in promoting liquid–liquid phase separation and fibrillation.