Efficient osteogenic differentiation of mesenchymal stem cells (MSCs) is a critical step in the treatment of bone defects and skeletal disorders, which present challenges for cell-based therapy and regenerative medicine. Thus, it is necessary to understand the regulatory agents involved in osteogenesis. Epigenetic mechanisms are considered to be the primary mediators that regulate gene expression during MSC differentiation. In recent years, epigenetic enzyme inhibitors have been used as epidrugs in cancer therapy. A number of studies mentioned the role of epigenetic inhibitors in the regulation of gene expression patterns related to osteogenic differentiation. This review attempts to provide an overview of the key regulatory agents of osteogenesis: transcription factors, signaling pathways, and, especially, epigenetic mechanisms. In addition, we propose to introduce epigenetic enzyme inhibitors (epidrugs) and their applications as future therapeutic approaches for bone defect regeneration.