Measles virus (MeV), a member of the paramyxovirus family of enveloped RNA viruses and one of the most infectious viral pathogens identified, accounts for major pediatric morbidity and mortality worldwide although coordinated efforts to achieve global measles control are in place. Target cell entry is mediated by two viral envelope glycoproteins, the attachment (H) and fusion (F) proteins, which form a complex that achieves merger of the envelope with target cell membranes. Despite continually expanding knowledge of the entry strategies employed by enveloped viruses, our molecular insight into the organization of functional paramyxovirus fusion complexes and the mechanisms by which the receptor binding by the attachment protein triggers the required conformational rearrangements of the fusion protein remain incomplete. Recently reported crystal structures of the MeV attachment protein in complex with its cellular receptors CD46 or SLAM and newly developed functional assays have now illuminated some of the fundamental principles that govern cell entry by this archetype member of the paramyxovirus family. Here, we review these advances in our molecular understanding of MeV entry in the context of diverse entry strategies employed by other members of the paramyxovirus family.