It was once suggested that adult or tissue-specific stem cells may be immortal; however, several recently published data suggest that their efficacy is limited by natural aging in common with most other somatic cell types. Decreased activity of stem cells in old age raises questions as to whether the age of the donor should be considered during stem cell transplantation and at what age the donor stem cells should be harvested to ensure the largest possible number of viable, functional, and non-altered stem cells. Although stem cells remain active into old age, changes in stem cells and their microenvironments inhibit their regenerative potential. The impact of aging on stem cell populations differs between tissues and depends on a number intrinsic and extrinsic factors, including systemic changes associated with immune system alterations. In this review, we describe key mechanisms of stem and progenitor cell aging and techniques that are currently used to identify signs of stem cells aging. Furthermore, we focus on the impact of aging on the capacity for proliferation, differentiation, and clinical use of stem cells. Finally, we detail the aging of embryonic, mesenchymal, and induced pluripotent stem cells, with particular emphasis on aging mechanisms and rejuvenation.