This review is focused on the recent development of various chitosan-based nanofibers (membranes, patches, mats, and scaffolds) that have been designed into core and shell structures using emulsion and coaxial electrospinning techniques. Chitosan, a promising polysaccharide derived from natural sources, holds potential for diverse applications, including nanofiber production, aimed at fostering sustainability. Core/shell chitosan-based nanofibers offer appealing features, including drug encapsulation and sustained release capabilities, with a higher efficiency than uniaxial fibers. The fabrication of core/shell chitosan-based nanofibers, including the co-spinning agents and various spinning parameters, such as spinning voltage, needle size, spinning flow rate, distance from needle tip to collector, temperature, and humidity, is summarized in this work. The review also explores updated applications in various fields, such as textiles, medical dressings, drug release systems, filtration membranes, and food packaging. It highlights the current advancements in core/shell chitosan-based nanofibers produced via electrospinning techniques. The innovative insights presented in the recent literature and the challenges associated with these sustainable materials are thoroughly examined, offering valuable contributions to the field.