Treatment of large segmental bone loss caused by fractures, osteomyelitis, and non-union results in expenses of around USD 300,000 per case. Moreover, the worst-case scenario results in amputation in 10% to 14.5% of cases. Biomaterials, cells, and regulatory elements are employed in bone tissue engineering (BTE) to create biosynthetic bone grafts with effective functionalization that can aid in the restoration of such fractured bones, preventing amputation and alleviating expenses. Chitin (CT) and chitosan (CS) are two of the most prevalent natural biopolymers utilized in the fields of biomaterials and BTE. To offer the structural and biochemical cues for augmenting bone formation, CT and CS can be employed alone or in combination with other biomaterials in the form of nanofibers (NFs). When compared with several fabrication methods available to produce scaffolds, electrospinning is regarded as superior since it enables the development of nanostructured scaffolds utilizing biopolymers. Electrospun nanofibers (ENFs) offer unique characteristics, including morphological resemblance to the extracellular matrix, high surface-area-to-volume ratio, permeability, porosity, and stability. This review elaborates on the recent strategies employed utilizing CT and CS ENFs and their biocomposites in BTE. We also summarize their implementation in supporting and delivering an osteogenic response to treat critical bone defects and their perspectives on rejuvenation. The CT- and CS-based ENF composite biomaterials show promise as potential constructions for bone tissue creation.