Plastic waste pollution is a global environmental problem that could be solved by biodegradable materials. In addition, its biodegradability has been important for medical applications. In this way, the biodegradability performance has been investigated for different materials under diversified environmental conditions. In this context, this review shows the main up-to-date biodegradable polymers (from renewable sources and fossil-based), their structure and properties, and their biodegradability characteristics. Also, this review shows the effect of polymer properties and environmental conditions on biodegradability, methods of biodegradability and toxicity determination, modification processes to enhance biodegradability, and main applications of biodegradable polymers for agriculture, medical, and packaging. Finally, this review presents a discussion of the implications of biodegradation on the environment, the current context, and future perspectives of plastic biodegradation.