In recent years, significant progress has been made in the development of polymeric materials, driving rapid expansion in associated industries and a surge in plastic production and usage. Consequently, the substantial generation of plastic waste has raised environmental concerns. One critical issue is the tendency of polymers to degrade over time, leading to disposal. Introducing self-healing systems capable of autonomously repairing damage caused by external factors can extend material lifespan, offering an effective means to mitigate polymer waste. The concept of self-healing draws inspiration from the regenerative abilities of living organisms. Extensive research over the past decade has led to significant advancements in self-healing materials, which can naturally repair and regain functionality using accessible resources. Various approaches, including physical, chemical, and physio-chemical methods, are employed in self-healing polymers. These self-healing mechanisms can be autonomic or triggered by external stimuli such as heat, solvent, or pressure. From thermosets to thermoplastics to elastomers, polymers of all types can exhibit self-healing properties. This review article delves into chemical approaches of fabricating self-healing synthetic polymers, focusing primarily on covalently cross-linked polymers with an emphasis on the Diels–Alder reaction. Additionally, the review offers a comprehensive discussion and compilation of different research works concerning other chemical approaches used in polymer self-healing.