This review describes the historical emergence of the concept of bone marrow mesenchymal stem cells (MSCs), summarizing data on Wolf and Trentin's hematopoietic inductive microenvironment; Dexter's hematopoiesis-supportive stromal cells; Friedenstein's osteogenic cells; and Pittenger's trilineal osteoblastic, chondrocytic, and adipocytic precursors; to finally introduce the specific bone marrow mesenchymal stem cells with differentiation potential to four lineages (mesenchymal and vascular smooth muscle lineages), and stromal and immunomodulatory capacities. Two points are the object of detailed discussion. The first point envisions the stem cell attributes (multipotentiality, self-renewal, tissue regeneration, population heterogeneity, plasticity, and lineage priming) compared with that of the paradigmatic hematopoietic stem cell. In the second point, we discuss the possible existence of bone marrow cells with greater differentiation potential, eventually pluripotential cells. The latter point raises the issues of cell fusion, reprogramming, or selection under nonstandardized conditions of rare populations of neuroectodermal origin, or of cells that had undergone mesenchymal-to-epithelial transition. In the last section, we review data on MSC senescence and possible malignant transformation secondary to extensive culture, gene transfer of telomerase, or mutations such as leading to Ewing's sarcoma. The set of data leads to the conclusion that bone marrow MSCs constitute a specific adult tissue stem cell population. The multiple characteristics of this stem cell type account for the versatility of the mechanisms of injured tissue repair. Although MSC administration may be extremely useful in a number of clinical applications, their transplantation is not without risks that must not be overlooked when developing cell therapy protocols.