Nonalcoholic steatohepatitis (NASH) is one of the most common chronic liver diseases in the world, yet no pharmacotherapies are available. The lack of translational animal models is a major barrier impeding elucidation of disease mechanisms and drug development. Multiple preclinical models of NASH have been proposed and can broadly be characterized as diet-induced, deficiency-induced, toxin-induced, genetically induced, or a combination of these. However, very few models develop advanced fibrosis while still reflecting human disease etiology or pathology, which is problematic since fibrosis stage is considered the best prognostic marker in patients and an important endpoint in clinical trials of NASH. While mice and rats predominate the NASH research, several other species have emerged as promising models. This review critically evaluates animal models of NASH, focusing on their ability to develop advanced fibrosis while maintaining their relevance to the human condition.