At the molecular level, aging is characterized by the accumulation of unresolved damage to essential components of cells, such as DNA, proteins, and organelles, which over time contributes to cellular malfunction and the onset of age-associated diseases. To counteract this detrimental process, cells are equipped with protective mechanisms that prevent or reverse molecular damage. Arguably, the cellular recycling process of autophagy is one of the most versatile repair pathways that cells display. Autophagy allows the degradation and recycling of surplus and/or damaged cytosolic components, which otherwise may pose a threat to cellular homeostasis. This is achieved via the delivery of cytoplasmic components to lysosomes, which are organelles equipped with a sophisticated set of degradative enzymes that eliminate cellular waste and transform it into building blocks to maintain cellular function. There are different autophagic routes, known as macroautophagy, microautophagy, and chaperone-mediated autophagy, via which a variety of cellular components, ranging from organelles, DNA, proteins, and lipids, can be delivered to lysosomes for proper turnover. While these autophagy pathways operate to maintain cellular homeostasis over time, an overall deficit in autophagic function leads to aging acceleration and is correlated with the onset of age-related diseases. However, the extent to which specific autophagic pathways and the selective degradation of cellular components contribute to aging, as well as the molecular interplay among the different routes, remain elusive and constitute a main research direction. This narrative review summarizes the implications of autophagy subtypes in aging, focusing on the contributions of each pathway to select cargo degradation and their interaction, and highlights future lines of research toward identifying potential therapeutic routes for the amelioration of selective autophagy to promote healthy aging.