Altered cellular homeostasis, accumulation of damaged non-functional organelles and presence of protein inclusions are characteristics shared by almost all types of differentiated cells in aged organisms. Cells rely on quality control mechanisms to prevent the occurrence of these events and the subsequent cellular compromise associated with them. What goes wrong in aging cells? Growing evidence supports gradual malfunctioning with age of the cellular quality control systems. In this review, we focus on autophagy, a catabolic process that contributes to the maintenance of cellular homeostasis through the degradation of unwanted and damaged components in lysosomes. We describe recent advances on the molecular characterization of this process, its different variants and the multiplicity of functions attributed to them. Autophagic dysfunction has been identified in severe human disorders, many of which worsen with age. We comment on the contribution of an adequate autophagic function to longevity, and the negative impact on health-span of the age-dependent decline in autophagic function.