Due to the increased public awareness in ensuring a sustainable and long-lasting world, both academic and industrial researchers are trying to use eco-friendly and biodegradable materials in every sphere of life. Petroleum-based synthetic materials are nonrenewable, hazardous, and costly. In contrast, natural fibers are mainly derived from plant-based sources, which are recyclable, renewable, sustainable, abundantly available, and cheap. Hence, the use of natural fibers in the fabrication of composite materials is increasing dramatically. These are used as a reinforcement with the polymer matrix to fabricate the composites. Although a massive amount of research works has been performed to develop green composites, until now the composite fabrication process is facing some terrific problems such as the lower adhesion tendency of the composites, due to the presence of the hydrophilic natural fibers and hydrophobic polymer matrix. Researchers are trying to find out the optimum combination of the composites that can be able to exhibit excellent mechanical properties for the application areas where greater strength is a must. This review is focusing on the composite materials fabricated from the bast fibers, a branch of the natural fibers, with various thermoplastic and thermosetting polymers, and their potential application areas.