Measles is a highly contagious disease, which was responsible for high infant mortality before the advent of an effective vaccine in 1963. In immunocompetent individuals, measles virus (MV) infection triggers an effective immune response that starts with innate responses and then leads to successful adaptive immunity, including cell-mediated immunity and humoral immunity. The virus is cleared and lifelong protection is acquired. However, changing epidemiology of measles due to vaccination as well as severe immunodeficiency has created new pockets of individuals vulnerable to measles. This chapter reviews the knowledge on effective measles-specific immune responses induced by natural infection and vaccination and explores problems arising in specific cases of immunodeficiency, infant immunity, and ineffective vaccination against measles.