Fiber-reinforced polymer composites are well-studied and established products, and today they are being used in different industrial and non-industrial areas. However, the increased interest in recyclability and the concerns about climate change caused materials scientists to look for a non-petroleum-based alternative to synthetic fibers and polymers. Since the beginning of this century, natural fibers and biopolymers have attracted increasing interest each year for composite applications. Thanks to this interest, studies on natural fibers and biopolymers have increased significantly. Despite the high number of studies on natural fibers and natural fiber-reinforced polymers (NFRP), there are gaps in the literature. This work reviews studies on natural fibers, biopolymers, and biocomposites with their advantages, disadvantages, and limitations. Studies that focus on the ways to reduce or eliminate these disadvantages and limitations have also been looked at. Also, current challenges and future perspectives for natural fibers, biopolymers, and NFRPs have been discussed.