Biodegradable polymers are gaining attention as alternatives to non-biodegradable plastics to address environmental issues. With the rising global demand for plastic products, the development of non-toxic, biodegradable plastics is a significant topic of research. Aliphatic polyester, the most common biodegradable polyester, is notable for its semi-crystalline structure and can be synthesized from fossil fuels, microbial fermentation, and plants. Due to great properties like being lightweight, biodegradable, biocompatible, and non-toxic, aliphatic polyesters are used in packaging, medical, agricultural, wearable devices, sensors, and textile applications. The biodegradation rate, crucial for biodegradable polymers, is discussed in this review as it is influenced by their structural properties and environmental conditions. This review discusses currently available biodegradable polyesters, their emerging applications, and the challenges in their commercialization. As research in this area grows, this review emphasizes the innovation in biodegradable aliphatic polyesters and their role in advancing environmental sustainability.