Nanofibers can mimic natural tissue structure by creating a more suitable environment for cells to grow, prompting a wide application of nanofiber materials. In this review, we include relevant studies and characterize the effect of nanofibers on mesenchymal stem cells, as well as factors that affect cell adhesion and osteogenic differentiation. We hypothesize that the process of bone regeneration in vitro is similar to bone formation and healing in vivo, and the closer nanofibers or nanofibrous scaffolds are to natural bone tissue, the better the bone regeneration process will be. In general, cells cultured on nanofibers have a similar gene expression pattern and osteogenic behavior as cells induced by osteogenic supplements in vitro. Genes involved in cell adhesion (focal adhesion kinase (FAK)), cytoskeletal organization, and osteogenic pathways (transforming growth factor-β (TGF-β)/bone morphogenic protein (BMP), mitogen-activated protein kinase (MAPK), and Wnt) are upregulated successively. Cell adhesion and osteogenesis may be influenced by several factors. Nanofibers possess certain physical properties including favorable hydrophilicity, porosity, and swelling properties that promote cell adhesion and growth. Moreover, nanofiber stiffness plays a vital role in cell fate, as cell recruitment for osteogenesis tends to be better on stiffer scaffolds, with associated signaling pathways of integrin and Yes-associated protein (YAP)/transcriptional co-activator with PDZ-binding motif (TAZ). Also, hierarchically aligned nanofibers, as well as their combination with functional additives (growth factors, HA particles, etc.), contribute to osteogenesis and bone regeneration. In summary, previous studies have indicated that upon sensing the stiffness of the nanofibrous environment as well as its other characteristics, stem cells change their shape and tension accordingly, regulating downstream pathways followed by adhesion to nanofibers to contribute to osteogenesis. However, additional experiments are needed to identify major signaling pathways in the bone regeneration process, and also to fully investigate its supportive role in fabricating or designing the optimum tissue-mimicking nanofibrous scaffolds.