Controlling measles outbreaks in the country of Georgia and throughout Europe is crucial for achieving the measles elimination goal for the World Health Organization’s European Region. However, large-scale measles outbreaks occurred in Georgia during 2013–2015 and 2017–2018. The epidemiology of these outbreaks indicates widespread circulation and genetic diversity of measles viruses and reveals persistent gaps in population immunity across a wide age range that have not been sufficiently addressed thus far. Historic problems and recent challenges with the immunization program contributed to outbreaks. Addressing population susceptibility across all age groups is needed urgently. However, conducting large-scale mass immunization campaigns under the current health system is not feasible, so more selective response strategies are being implemented. Lessons from the measles outbreaks in Georgia could be useful for other countries that have immunization programs facing challenges related to health-system transitions and the presence of age cohorts with historically low immunization coverage.