In 1980, Ludwig and colleagues described a series of patients with liver histology characterized by the accumulation of fat and the presence of hepatic necroinflammation in the absence of a history of excessive alcohol consumption. They coined the term nonalcoholic steatohepatitis (NASH), which today is regarded as one of the most common causes of liver disease in affluent countries. NASH is a subset of a larger spectrum of diseases termed fatty liver disease (including alcoholic and nonalcoholic fatty liver disease; AFLD and NAFLD, respectively). NAFLD and NASH are linked to visceral adiposity, insulin resistance, dyslipidemia and type 2 diabetes, and are increasing due to the prevalence of the metabolic syndrome. In this context, research has been undertaken using animals to model human steatosis and NAFLD to NASH disease progression. This Review discusses the prevalent dietary and inflammation-based genetic animal models described in recent years.