Biodegradable polymers are increasingly recognized as key enablers of sustainable additive manufacturing (AM), offering a unique combination of environmental degradability, tunable mechanical performance, and compatibility across diverse printing platforms. This review examines recent advances in the molecular design, composite formulation, and 3D printing of biodegradable thermoplastics, including PLA, PCL, PBAT, and PBS, across major AM platforms such as fused deposition modeling (FDM), direct ink writing (DIW), and digital light processing (DLP). Particular emphasis is placed on structure–property–function–degradation relationships that influence rheological behavior, interlayer adhesion, mechanical anisotropy, and life cycle performance. Material engineering strategies, including polymer blending, reactive compatibilization, nanofiller reinforcement, and platform-specific parameter optimization, are critically examined for their capacity to enhance print fidelity and enable precise control over degradation kinetics. Representative applications in biomedical scaffolds, controlled drug delivery systems, agricultural devices, and compostable packaging demonstrate how deliberate material-process integration can achieve both functional performance and temporally programmed degradation. Furthermore, sustainable design paradigms, such as design for degradation, life cycle synchronization, topology-driven material minimization, and circular manufacturing frameworks, are discussed as essential for transitioning AM from rapid prototyping to responsible large-scale production. Despite substantial progress, challenges remain in mechanical robustness, material standardization, and end-of-life infrastructure. Addressing these limitations will require coordinated advances in polymer chemistry, processing science, and life cycle engineering to establish truly circular, high-performance biodegradable AM systems.