With more than 71 million chronically infected people, the hepatitis C virus (HCV) is a major global health concern. Although new direct acting antivirals have significantly improved the rate of HCV cure, high therapy cost, potential emergence of drug-resistant viral variants, and unavailability of a protective vaccine represent challenges for complete HCV eradication. Relevant animal models are required, and additional development remains necessary, to effectively study HCV biology, virus-host interactions and for the evaluation of new antiviral approaches and prophylactic vaccines. The chimpanzee, the only non-human primate susceptible to experimental HCV infection, has been used extensively to study HCV infection, particularly to analyze the innate and adaptive immune response upon infection. However, financial, practical, and especially ethical constraints have urged the exploration of alternative small animal models. These include different types of transgenic mice, immunodeficient mice of which the liver is engrafted with human hepatocytes (humanized mice) and, more recently, immunocompetent rodents that are susceptible to infection with viruses that are closely related to HCV. In this review, we provide an overview of the currently available animal models that have proven valuable for the study of HCV, and discuss their main benefits and weaknesses.