Autophagy, or cellular self-digestion, is a catabolic process that targets cell constituents including damaged organelles, unfolded proteins, and intracellular pathogens to lysosomes for degradation. Autophagy is crucial for development, differentiation, survival, and homeostasis. Important links between the regulation of autophagy and liver complications associated with obesity, non-alcoholic fatty liver disease (NAFLD), have been reported. The spectrum of these hepatic abnormalities extends from isolated steatosis to non-alcoholic steatohepatitis (NASH), steatofibrosis, which sometimes leads to cirrhosis, and hepatocellular carcinoma. NAFLD is one of the three main causes of cirrhosis and increases the risk of liver-related death and hepatocellular carcinoma. The pathophysiological mechanisms of the progression of a normal liver to steatosis and then more severe disease are complex and still unclear. The regulation of the autophagic flux, a dynamic response, and the knowledge of the role of autophagy in specific cells including hepatocytes, hepatic stellate cells, immune cells, and hepatic cancer cells have been extensively studied these last years. This review will provide insight into the current understanding of autophagy and its role in the evolution of the hepatic complications associated with obesity, from steatosis to hepatocellular carcinoma.