Measles is one of the most contagious diseases known to man. Despite the existence of a safe and effective live attenuated vaccine, measles can appear in vaccinated individuals. Paradoxically, breakthrough cases increase as vaccination coverage in the general population rises. In measles endemic areas, breakthrough cases represent less than 10% of total infections, while in areas with high vaccination coverage these are over 10% of the total. Two different vaccination failures have been described: primary vaccination failure, which consists in the complete absence of humoral response and occurs in around 5% of vaccinated individuals; and secondary vaccination failure is due to waning immunity or incomplete immunity and occurs in 2–10% of vaccinees. Vaccination failures are generally associated with lower viral loads and milder disease (modified measles) since vaccination limits the risk of complicated disease. Vaccination failure seems to occur between six and twenty-six years after the last vaccine dose administration. This review summarizes the literature about clinical, serological, epidemiological, and molecular characteristics of measles breakthrough cases and their contribution to virus transmission. In view of the measles elimination goal, the assessment of the potential decline in antibody protection and the targeted implementation of catch-up vaccination are essential.