Bone-tissue engineering is an alternative treatment for bone defects with great potential in which scaffold is a critical factor to determine the effect of bone regeneration. Electrospun nanofibers are widely used as scaffolds in the biomedical field for their similarity with the structure of the extracellular matrix (ECM). Their unique characteristics are: larger surface areas, porosity and processability; these make them ideal candidates for bone-tissue engineering. This review briefly introduces bone-tissue engineering and summarizes the materials and methods for electrospining. More importantly, how to functionalize electrospun nanofibers to make them more conducive for bone regeneration is highlighted. Finally, the existing deficiencies of functionalized electrospun nanofibers for promoting osteogenesis are proposed. Such a summary can lay the foundation for the clinical practice of functionalized electrospun nanofibers.