Skeletal-related disorders such as arthritis, bone cancer, osteosarcoma, and osteoarthritis are among the most common reasons for mortality in humans at present. Nanostructured scaffolds have been discovered to be more efficient for bone regeneration than macro/micro-sized scaffolds because they sufficiently permit cell adhesion, proliferation, and chemical transformation. Nanofibrous scaffolds mimicking artificial extracellular matrices provide a natural environment for tissue regeneration owing to their large surface area, high porosity, and appreciable drug loading capacity. Here, we review recent progress and possible future prospective electrospun nanofibrous scaffolds for bone tissue engineering. Electrospun nanofibrous scaffolds have demonstrated promising potential in bone tissue regeneration using a variety of nanomaterials. This review focused on the crucial role of electrospun nanofibrous scaffolds in biological applications, including drug/growth factor delivery to bone tissue regeneration. Natural and synthetic polymeric nanofibrous scaffolds are extensively inspected to regenerate bone tissue. We focused mainly on the significant impact of nanofibrous composite scaffolds on cell adhesion and function, and different composites of organic/inorganic nanoparticles with nanofiber scaffolds. This analysis provides an overview of nanofibrous scaffold-based bone regeneration strategies; however, the same concepts can be applied to other organ and tissue regeneration tactics.