This is a review of the current status of knowledge on adult stem cells as well as the criteria and evidence for their potential to transform into different cell types and cell lineages. Reports on stem cell sources, focusing on tissues from adult subjects, were also investigated. Numerous reports have been published on the search for early markers of both stem cells and the precursors of various cell lineages. The question is still open about the characteristics of the primary stem cell. The existing proofs and hypotheses have not yielded final solutions to this problem. From a practical point of view it is also crucial to find a minimal set of markers determining the phenotypes of the precursor cells of a particular cell lineage. Several lines of evidence seem to bring closer the day when we will be able to detect the right stem cell niche and successfully isolate precursor cells that are needed for the treatment of a particular disorder. Recent reports on cases of cancer in patients subjected to stem cell therapy are yet another controversial issue looked into in this review, although the pros and cons emerging from the results of published studies still do not provide satisfying evidence to fully understand this issue.