Most multicellular organisms are known to age, due to accumulation of damage and other deleterious changes over time. These changes are often irreversible, as organisms, humans included, evolved fully differentiated, irreplaceable cells (e.g. neurons) and structures (e.g. skeleton). Hence, deterioration or loss of at least some cells and structures should lead to inevitable aging of these organisms. Yet, some cells may escape this fate: adult somatic cells may be converted to partially reprogrammed cells or induced pluripotent stem cells (iPSCs). By their nature, iPSCs are the cells representing the early stages of life, indicating a possibility of reversing the age of cells within the organism. Reprogramming strategies may be accomplished both in vitro and in vivo, offering opportunities for rejuvenation in the context of whole organisms. Similarly, older organs may be replaced with the younger ones prepared ex vivo, or grown within other organisms or even other species. How could the irreversibility of aging of some parts of the organism be reconciled with the putative reversal of aging of the other parts of the same organism? Resolution of this question holds promise for dramatically extending lifespan, which is currently not possible with traditional genetic, dietary and pharmacological approaches. Critical issues in this challenge are the nature of aging, relationship between aging of an organism and aging of its parts, relationship between cell dedifferentiation and rejuvenation, and increased risk of cancer that goes hand in hand with rejuvenation approaches.