Biodegradable synthetic polymers have become key materials in modern controlled drug delivery systems due to their tunable physicochemical properties and predictable degradation behavior. This review critically discusses three of the most widely used polymers—poly(lactic-co-glycolic acid) (PLGA), poly(ε-caprolactone) (PCL), and polyethylene glycol (PEG)—with emphasis on their degradation mechanisms, structure–property relationships, and implications for drug release and clinical performance. PLGA undergoes hydrolytic degradation into biocompatible lactic and glycolic acids, with degradation rate and release profiles strongly influenced by molecular weight, monomer ratio, and end-group chemistry. PCL, owing to its high crystallinity and hydrophobicity, degrades more slowly via bulk or surface erosion, making it suitable for long-term delivery depots and tissue-engineering applications. PEG, particularly in hydrogel-based systems, degrades primarily through crosslink cleavage, enabling diffusion- and degradation-controlled release while maintaining a non-acidic environment favorable for sensitive biomolecules. Advances in amphiphilic block copolymers, such as PLGA–PEG–PLGA, PCL–PEG–PCL, and PEG-based hybrid systems, further enhance drug solubilization, micellization, and stimuli-responsive behavior, allowing precise and sustained delivery. Overall, this review highlights how a comprehensive understanding of polymer degradation mechanisms and structural design is essential for developing next-generation drug delivery systems with improved safety, stability, and therapeutic efficacy.