Hepatocellular carcinoma (HCC) is the most common type of primary liver cancer and one of the deadliest cancers worldwide. Despite extensive research, the biological mechanisms underlying HCC’s development and progression remain only partially understood. Chronic overeating and/or sedentary-lifestyle-associated obesity, which promote Non-Alcoholic Fatty Liver Disease (NAFLD), have recently emerged as worrying risk factors for HCC. NAFLD is characterized by excessive hepatocellular lipid accumulation (steatosis) and affects one quarter of the world’s population. Steatosis progresses in the more severe inflammatory form, Non-Alcoholic Steatohepatitis (NASH), potentially leading to HCC. The incidence of NASH is expected to increase by up to 56% over the next 10 years. Better diagnoses and the establishment of effective treatments for NAFLD and HCC will require improvements in our understanding of the fundamental mechanisms of the disease’s development. This review describes the pathogenesis of NAFLD and the mechanisms underlying the transition from NAFL/NASH to HCC. We also discuss a selection of appropriate preclinical models of NAFLD for research, from cellular models such as liver-on-a-chip models to in vivo models, focusing particularly on mouse models of dietary NAFLD-HCC.