Regenerative medicine is searching for stem cells that can be safely and efficiently employed for regeneration of damaged solid organs (e.g., the heart, brain, or liver). Ideal for this purpose would be pluripotent stem cells, which, according to their definition, have broad potential to differentiate into all types of adult cells. For almost 20 years, there have been unsuccessful attempts to harness controversial embryonic stem cells (ESCs) isolated from embryos. Induced pluripotent stem cells (iPSCs), generated by genetic modification of adult somatic cells, are a more promising source. However, both iPSC and ESCs are associated with a risk of teratoma formation. At the same time, various types of more‑differentiated adult stem and progenitor cells derived from the bone marrow, umbilical cord blood, mobilized peripheral blood, or fat tissue are being employed in clinical trials to regenerate damaged solid organs. However, for most of these cells, there is a lack of convincing documentation for successful regeneration of the treated organs. Beneficial effects of those cells might be explained by paracrine effects of growth factors, cytokines, chemokines, bioactive lipids, and extracellular microvesicles, which are released from the cells and have trophic, antiapoptotic, and angiopoietic effects. Nevertheless, there is evidence that adult tissues harbor a promising population of very rare dormant stem cells with broad differentiation potential. In this review, we will discuss various potential sources of stem cells for regenerative medicine and the mechanisms that explain some of their beneficial effects as well as highlight the results of the first clinical trials.