Hepatitis C is a disease for which in approximately 30 years we have gone from the discovery of the causative agent in 1989, to the introduction of direct-acting antiviral (DAAs) therapies starting from 2011, and to a proposal for its elimination in 2016, with some countries being on track for this goal. Elimination efforts, in the absence of a vaccine, rely on prevention measures and antiviral therapies. However, treatment rates have declined in recent years and are not considered adequate to achieve this goal at a global level. This poses a great epidemiological challenge, as HCV in many countries still causes a significant burden and most infected people are not yet diagnosed. Consequently, efforts are needed at different levels with common purposes: to facilitate access to screening and diagnosis and to improve linkage to care pathways. In this review, we discuss the latest epidemiological findings on HCV infection, the obstacles to its elimination, and strategies that are believed to be useful to overcome these obstacles but are applied unevenly across the world.