Fiber-reinforced polymer composites (FRCs) from renewable and biodegradable fiber and sustainable polymer resins have gained substantial attention for their potential to mitigate environmental impacts. The limitations of these composites become evident when considered in the context of high-performance engineering applications, where synthetic fiber composites like glass or carbon FRCs typically dominate. A balance between the performance of the composite and biodegradability is imperative in the pursuit of what may be termed an environmentally conscious composite. This comprehensive review article provides some insight into the sustainability of FRCs, alongside detailing the sustainability considerations at various stages—materials, performance, applications, and end of life. The discussion also covers the different types of sustainable natural fibers and the types of polymer resins with some of the current achievements in the mechanical and functional properties of such composites, followed by a broad survey of their potential applications across diverse engineering applications.