Despite the availability of safe and effective vaccines against measles and several animal morbilliviruses, they continue to cause regular outbreaks and epidemics in susceptible populations. Morbilliviruses are highly contagious and share a similar pathogenesis in their respective hosts. This review provides an overview of morbillivirus history and the general replication cycle and recapitulates Morbillivirus pathogenesis focusing on common and unique aspects seen in different hosts. It also summarizes the state of knowledge regarding virus-host interactions on the cellular level with an emphasis on viral interference with innate immune response activation, and highlights remaining knowledge gaps.