The maintenance of the proteome is essential to preserve cell functionality and the ability to respond and adapt to the changing environment. This is regulated by the proteostasis network, a dedicated set of molecular components comprised of molecular chaperones and protein clearance mechanisms, regulated by cell stress signaling pathways, that prevents the toxicity associated with protein misfolding and accumulation of toxic aggregates in different subcellular compartments and tissues. The efficiency of the proteostasis network declines with age and this failure in protein homeostasis has been proposed to underlie the basis of common age-related human disorders. The current advances in the understanding of the mechanisms and regulation of proteostasis and of the different types of digressions in this process in aging have turned the attention toward the therapeutic opportunities offered by the restoration of proteostasis in age-associated degenerative diseases. Here, we discuss some of the unresolved questions on proteostasis that need to be addressed to enhance healthspan and to diminish the pathology associated with persistent protein damage.