The increasing environmental concerns regarding conventional plastics have led to a growing demand for sustainable alternatives, such as biodegradable plastics. Yeast cell factories, specifically Saccharomyces cerevisiae and Yarrowia lipolytica, have emerged as promising platforms for bioplastic production due to their scalability, robustness, and ease of manipulation. This review highlights synthetic biology approaches aimed at developing yeast cell factories to produce key biodegradable plastics, including polylactic acid (PLA), polyhydroxyalkanoates (PHAs), and poly (butylene adipate-co-terephthalate) (PBAT). We explore recent advancements in engineered yeast strains that utilize various synthetic biology strategies, such as the incorporation of new genetic elements at the gene, pathway, and cellular system levels. The combined efforts of metabolic engineering, protein engineering, and adaptive evolution have enhanced strain efficiency and maximized product yields. Additionally, this review addresses the importance of integrating computational tools and machine learning into the Design-Build-Test-Learn cycle for strain development. This integration aims to facilitate strain development while minimizing effort and maximizing performance. However, challenges remain in improving strain robustness and scaling up industrial production processes. By combining advanced synthetic biology techniques with computational approaches, yeast cell factories hold significant potential for the sustainable and scalable production of bioplastics, thus contributing to a greener bioeconomy.