Unsaturated polyester resin (UPR) is one of the first commercialized polymer matrices for composites reinforced with glass fibers, but has remained popular to this day. To reduce their environmental impact, natural fibers have been used as reinforcements. Researchers all over the world are still interested in these composites, and numerous papers have been published in the last four decades. Using bibliometric analysis, this work provides compiled, structured, and relevant information about the evolution and current state of these materials. This first study on UPR biocomposites based on bibliometric analysis examined 531 published papers identified in the Scopus database from 1982 to July 2022. An analysis of the most active states, leading institutions, and leading authors is followed by the identification of key areas such as the most common natural fibers used as reinforcements, fiber treatments, and composite design parameters such as processing techniques; recently, composite testing; and technological applications. The findings emphasize the importance of staying active in this global field and provide information on novel promising topics for future research.