AIDS among persons who inject drugs, first identified in December 1981, has become a global epidemic. Injecting drug use has been reported in 148 countries and HIV infection has been seen among persons who inject drugs in 61 countries. Many locations have experienced outbreaks of HIV infection among persons who inject drugs, under specific conditions that promote very rapid spread of the virus. In response to these HIV outbreaks, specific interventions for persons who inject drugs include needle/syringe exchange programs, medicated assisted treatment (with methadone or buprenorphine) and antiretroviral therapy. Through a “combined prevention” approach, these interventions significantly reduced new HIV infections among persons who inject drugs in several locations including New York City, Vancouver and France. The efforts effectively ended the local HIV epidemic among persons who inject drugs in those locations. This review examines possible processes through which combined prevention programs may lead to ending HIV epidemics. However, notable outbreaks of HIV among persons who inject drugs have recently occurred in several countries, including in Athens, Greece, Tel-Aviv, Israel, Dublin Ireland, as well as in Scott County, Indiana USA. This review also considers different factors that may have led to these outbreaks. We conclude with addressing the remaining challenges for reducing HIV infection among persons who inject drugs.