The immune system deploys a complex network of cells and signaling pathways to protect host integrity against exogenous threats, including measles virus (MeV). However, throughout its evolutionary path, MeV developed various mechanisms to disrupt and evade immune responses. Despite an available vaccine, MeV remains an important re-emerging pathogen with a continuous increase in prevalence worldwide during the last decade. Considerable knowledge has been accumulated regarding MeV interactions with the innate immune system through two antagonistic aspects: recognition of the virus by cellular sensors and viral ability to inhibit the induction of the interferon cascade. Indeed, while the host could use several innate adaptors to sense MeV infection, the virus is adapted to unsettle defenses by obstructing host cell signaling pathways. Recent works have highlighted a novel aspect of innate immune response directed against MeV unexpectedly involving DNA-related sensing through activation of the cGAS/STING axis, even in the absence of any viral DNA intermediate. In addition, while MeV infection most often causes a mild disease and triggers a lifelong immunity, its tropism for invariant T-cells and memory T and B-cells provokes the elimination of one primary shield and the pre-existing immunity against previously encountered pathogens, known as “immune amnesia”.