Molecular genetic mechanisms, signaling pathways, cultural conditions, factors, and markers of osteogenic differentiation of mesenchymal stem cells (MSC) are actively studied despite numerous works in this area of cellular technologies. This is largely due to the accumulating contradictions in seemingly classical knowledge, as well as permanent updating of the results in the field. In this regard, we focused on the main classical concepts and some new factors and mechanisms that have a noticeable regulatory effect on the differentiation potential of postnatal MSCs. The present review considers the significance of MSC sources for their differentiation capacity, as well as the role of the cellular microenvironment. The issues of classification, terminology, and functional activity of MSCs from various sources are discussed. The paracrine potential of MSCs in tissue regeneration has been considered; sufficient importance of inflammation in osteogenesis is noted, in particular, the presence of inflammatory cytokines and chemokines in the lesion focus, produced not only by microenvironmental cells but also by blood cells, including mononuclear leukocytes, migrating to the affected site. An important role in this review is given to biomechanical signals and to influence of conformational changes in cell cytoskeleton (cell shape) upon MSC differentiation, since the morphological features of cells and the structure of cytoskeleton are modulated by interactions of the cell surface with environmental factors, including hydrostatic pressure, fluid flow, compression/stretching loads. The data are presented concerning elasticity of extracellular matrix being a determining factor of cell differentiation. We conclude that one should switch from point studies of individual gene effects to multiple measurements of the gene-regulatory profile and biomolecules responsible for multiple, still poorly studied osteogenic factors of endogenous and exogenous origin. Among cornerstones in future (epi)genetic studies will be to decide if osteomodulatory effects are realized through specific signaling pathways and/or via cross-signaling with known genes controlling osteogenic differentiation of MSCs.