There is a shortage of suitable tissue-engineered solutions for gingival recession, a soft tissue defect of the oral cavity. Autologous tissue grafts lead to an increase in morbidity due to complications at the donor site. Although material substitutes are available on the market, their development is early, and work to produce more functional material substitutes is underway. The latter materials along with newly conceived tissue-engineered substitutes must maintain volumetric form over time and have advantageous mechanical and biological characteristics facilitating the regeneration of functional gingival tissue. This review conveys a comprehensive and timely perspective to provide insight towards future work in the field, by linking the structure (specifically multilayered systems) and function of electrospun material-based approaches for gingival tissue engineering and regeneration. Electrospun material composites are reviewed alongside existing commercial material substitutes’, looking at current advantages and disadvantages. The importance of implementing physiologically relevant degradation profiles and mechanical properties into the design of material substitutes is presented and discussed. Further, given that the broader tissue engineering field has moved towards the use of pre-seeded scaffolds, a review of promising cell options, for generating tissue-engineered autologous gingival grafts from electrospun scaffolds is presented and their potential utility and limitations are discussed.