Autophagy is an evolutionarily conserved cellular process, through which damaged organelles and superfluous proteins are degraded, for maintaining the correct cellular balance during stress insult. It involves formation of double-membrane vesicles, named autophagosomes, that capture cytosolic cargo and deliver it to lysosomes, where the breakdown products are recycled back to cytoplasm. On the basis of degraded cell components, some selective types of autophagy can be identified (mitophagy, ribophagy, reticulophagy, lysophagy, pexophagy, lipophagy, and glycophagy). Dysregulation of autophagy can induce various disease manifestations, such as inflammation, aging, metabolic diseases, neurodegenerative disorders and cancer. The understanding of the molecular mechanism that regulates the different phases of the autophagic process and the role in the development of diseases are only in an early stage. There are still questions that must be answered concerning the functions of the autophagy-related proteins. In this review, we describe the principal cellular and molecular autophagic functions, selective types of autophagy and the main in vitro methods to detect the role of autophagy in the cellular physiology. We also summarize the importance of the autophagic behavior in some diseases to provide a novel insight for target therapies.