Autophagy is a catabolic process conserved among all eukaryotes essential for the cellular and organismal homeostasis. One of the principal roles of this pathway is to maintain an accurate balance between synthesis, degradation and subsequent recycling of cellular components. Under certain conditions, however, cells are also able to modulate autophagy and specifically remove a number of structures that are potentially harmful. Aberrant protein aggregates, damaged organelles or pathogens can be selectively incorporated into large double-membrane vesicles called autophagosomes to be delivered into lysosomes for destruction. This ability to eliminate specific structures is exploited by the cells in several physiological processes as well as in multiple pathological situations, making autophagy a precious multitask cellular degradative pathway. In this review, we will first examine what is known about the basic mechanisms of autophagy and then discuss in a second part the nature of the cargoes that are selectively sequestered into autophagosomes, what provides the specificity and the possible implications of selective types of autophagy in human pathologies.