Macroautophagy (hereafter referred to as autophagy), a highly conserved metabolic process, regulates cellular homeostasis by degrading dysfunctional cytosolic constituents and invading pathogens via the lysosomal system. In addition, autophagy selectively recycles specific organelles such as damaged mitochondria (via mitophagy), and lipid droplets (LDs; via lipophagy) or eliminates specialized intracellular pathogenic microorganisms such as hepatitis B virus (HBV) and coronaviruses (via virophagy). Selective autophagy, particularly mitophagy, plays a key role in the preservation of healthy liver physiology, and its dysfunction is connected to the pathogenesis of a wide variety of liver diseases. For example, lipophagy has emerged as a defensive mechanism against chronic liver diseases. There is a prominent role for mitophagy and lipophagy in hepatic pathologies including non-alcoholic fatty liver disease (NAFLD), hepatocellular carcinoma (HCC), and drug-induced liver injury. Moreover, these selective autophagy pathways including virophagy are being investigated in the context of viral hepatitis and, more recently, the coronavirus disease 2019 (COVID-19)-associated hepatic pathologies. The interplay between diverse types of selective autophagy and its impact on liver diseases is briefly addressed. Thus, modulating selective autophagy (e.g., mitophagy) would seem to be effective in improving liver diseases. Considering the prominence of selective autophagy in liver physiology, this review summarizes the current understanding of the molecular mechanisms and functions of selective autophagy (mainly mitophagy and lipophagy) in liver physiology and pathophysiology. This may help in finding therapeutic interventions targeting hepatic diseases via manipulation of selective autophagy.