In recent years, a variety of novel materials and processing technologies have been developed to prepare tissue engineering scaffolds for bone defect repair. Among them, nanofibers fabricated via electrospinning technology have attracted much interest owing to the unique feature of highly mimicking the natural bone extracellular matrix. In particular, many achievements have been made in this field over the past several years. Therefore, this review aims to summarize the most recent advances and highlights of electrospun nanofibers in bone regeneration applications, by focusing on their material compositions (synthetic polymers, natural polymers, composite nanofibers, and hybrid nanofibers), structural regulation strategies (aligned structures, core-shell structures, gradient structures, and three-dimensional structures), function regulation achievements (biomineralization, osteogenesis, vascularization, immunomodulatory, and anti-infection), and combination with other emerging scaffold fabrication technologies (3D printing, electrospraying, and microfluidics). Finally, the future challenges of nanofibrous scaffolds in this field are also discussed briefly. It is anticipated that this review will provide useful insights into the future development of nanofibrous scaffolds in tissue engineering and bone regeneration applications.