The autophagy–lysosome pathway is a highly conserved bulk degradation system in eukaryotes. During starvation, cytoplasmic constituents are non-selectively degraded by autophagy, and the resulting amino acids are utilized for cell survival. By taking advantage of mouse genetics, many physiological functions of mammalian autophagy have been uncovered. Growing lines of evidences have revealed the essential role of constitutive (or basal) autophagy in cellular homeostasis through its selectivity. p62, one of the selective substrates for autophagy, plays a key role in the formation of cytoplasmic proteinaceous inclusion, a hallmark of conformational diseases such as Alzheimer’s disease, Parkinson’s disease, and various chronic liver disorders. In this review, we discuss the physiological roles of the selective turnover of p62 by autophagy and their molecular mechanisms.