Food is fundamental to human survival, health, culture, and well-being. In response to the increasing demand for sustainable food preservation, chitosan (CS)-based electrospun nanofibers have emerged as promising materials due to their biodegradability, biocompatibility, and inherent antimicrobial properties. When combined with other biopolymers or bioactive compounds, CS-based nanofibers offer enhanced functionality for applications in food packaging, preservation, and additives. This review summarizes recent advances in the fabrication and performance of CS-polymer and CS-inorganic composite nanofibers, with a focus on their mechanical strength, thermal stability, barrier properties, and antimicrobial efficacy. The use of these nanofibers across a range of food categories—including vegetables, fruits, fresh-cut produce, dairy products, meat, seafood, and nuts—is examined. Beyond experimental approaches, the review also explores the growing role of computational simulations in predicting the mechanical strength, barrier performance, antimicrobial activity, and biodegradability of CS-based nanofibers. Key modeling techniques and simulation tools are summarized. Finally, current challenges and future research directions are discussed, underscoring the potential of CS-based electrospun nanofibers as sustainable and multifunctional solutions for modern food packaging. By integrating experimental advancements with computational insights, this review provides a comprehensive and forward-looking perspective on CS-based electrospun nanofibers for food packaging.