Some internal and external stimuli elicit stress responses on the cellular level and at the level of the organism. When the stimulus is brief and its intensity mild to moderate, it triggers adaptation changes that improve the cell's or organism's survival. This adaptation is achieved through a variety of cellular mechanisms such as induction of repair mechanisms, improved removal of damaged macromolecules, upregulation of endogenous antioxidant defenses, and prevention of apoptosis triggering by moderate stressors. The key intracellular signaling pathways involved in stress adaptation are the mTORC1 and SIRT1. Manipulating these stress adaptation signaling pathways with a variety of agents, improves the cellular adaptation to stress, prolongs cell survival, and improves the transplantation outcome in animal models and in clinical trials. The challenge for the future is to fine-tune the numerous experimental techniques to suit the needs of transplantation and regenerative medicine.