The increasing demand for sustainable and high-performance polymeric materials has stimulated extensive research into renewable feedstocks as alternatives to petroleum-derived resources. Among various renewable resources, vegetable oils have emerged as versatile platforms for the development of functional polymeric materials because of their abundance, structural diversity, relatively low toxicity, and potential for chemical modification. Although substantial research has focused on the synthesis and functionalization of vegetable-oil-derived polymers, increasing attention is now being directed toward their practical performance and application in industrially relevant environments. This review presents an application-oriented assessment of functional polymer systems derived from vegetable oils, emphasizing their performance, technological potential, industrial relevance, and remaining challenges. Applications in protective coatings, corrosion-resistant and self-healing surfaces, polyurethane and non-isocyanate polyurethane materials, adhesives and sealants, thermosetting resins, composites, elastomers, lubricants, packaging, biomedical materials, and additive manufacturing are discussed. Particular attention is given to application-specific properties including adhesion, hardness, flexibility, thermal stability, chemical resistance, barrier performance, mechanical strength, durability, and self-healing behavior. The potential of vegetable-oil-derived polymers for multifunctional and smart materials is also highlighted. In addition, challenges associated with feedstock variability, functionalization efficiency, performance consistency, processing, scale-up, cost, long-term durability, standardization, and end-of-life management are critically considered. The transition from laboratory-scale materials to industrial products requires not only increased renewable content but also application-specific performance validation, life-cycle assessment, economic evaluation, and compatibility with existing manufacturing infrastructure. Future research should therefore focus on high-performance multifunctional materials, scalable processing, non-toxic chemistry, standardized testing, circularity, and industrial demonstration. Vegetable-oil-derived functional polymers have significant potential to contribute to sustainable material technologies when renewable feedstocks are integrated with rational molecular design and application-driven engineering.