As measles virus causes subacute sclerosing panencephalitis and measles inclusion body encephalitis due to its ability to establish human persistent infection, without symptoms for the time between the acute infection and the onset of clinical symptoms, it has been the paradigm for a long term persistent as opposed to chronic infection by an RNA virus. We have reviewed the mechanisms of persistence of the virus and discuss specific mutations associated with CNS infection affecting the matrix and fusion protein genes. These are placed in the context of our current understanding of the viral replication cycle. We also consider the proposed mechanisms of persistence of the virus in replicating cell cultures and conclude that no general mechanistic model can be derived from our current state of knowledge. Finally, we indicate how reverse genetics approaches and the use of mouse models with specific knock-out and knock-in modifications can further our understanding of measles virus persistence.