The measles virus replication complex represents a potentially important, but as yet relatively unexplored target for viral inhibition. Little is known about the molecular mechanisms that underpin replication and transcription in paramyxoviruses. In recent years it has become clear that conformational dynamics play an important role in paramyxoviral replication, and that a complete understanding of the viral cycle requires a description of the structural plasticity of the different components. Here, we review recent progress in this direction, covering the dynamics of the nucleocapsid assembly process, high resolution structure and dynamics of protein:RNA interactions, and the investigation of the role of intrinsic conformational disorder in pre-assembly nucleoprotein/phosphoprotein complexes. Finally, we discuss the role of viral factories in the form of phase-separated membraneless organelles formed by measles virus phospho and nucleoproteins that promote the assembly of nucleocapsid structures.