<p>In the contemporary era of sustainable materials research, the replacement of petroleum-derived plastics with biodegradable and renewable alternatives has gained paramount importance, particularly in the packaging sector. Among the potential substitutes, paper is considered a promising candidate due to its cellulose-based structure, inherent biodegradability, and recyclability. However, its poor resistance to moisture, oxygen, grease, and oils imposes significant restrictions on its widespread application in functional packaging. To address these limitations, surface coatings have emerged as a practical solution. Traditionally, paper substrates have been laminated or coated with non-biodegradable polymers such as polyethylene (PE) and polypropylene (PP), which substantially hinder the biodegradation process and contribute to environmental burden. Consequently, research has shifted towards the utilization of bio-based and biodegradable aliphatic polyesters as sustainable coating materials. This review highlights the potential of six major aliphatic polyesters, polylactic acid (PLA), polycaprolactone (PCL), polybutylene adipate terephthalate (PBAT), polybutylene succinate (PBS), polyhydroxybutyrate (PHB), and polyhydroxybutyrate-co-valerate (PHBV) as eco-friendly coatings for paper packaging. Particular emphasis is placed on their intrinsic barrier characteristics, processing challenges, and strategies to overcome brittleness and crystallization issues. Additionally, the review discusses advancements in polymer blending, copolymerization, and the incorporation of functional fillers or nanomaterials to enhance the barrier, thermal, and mechanical performance of coated paper and paperboard. Collectively, these insights aim to provide a comprehensive perspective on the development of fully biodegradable, high-performance paper-based packaging materials.</p>