The goal of this review is to map the current state of biodegradable materials that are used in tissue engineering for a variety of applications. At the beginning, the paper briefly identifies typical clinical indications in orthopedics for the use of biodegradable implants. Subsequently, the most frequent groups of biodegradable materials are identified, classified, and analyzed. To this end, a bibliometric analysis was applied to evaluate the evolution of the scientific literature in selected topics of the subject. The special focus of this study is on polymeric biodegradable materials that have been widely used for tissue engineering and regenerative medicine. Moreover, to outline current research trends and future research directions in this area, selected smart biodegradable materials are characterized, categorized, and discussed. Finally, pertinent conclusions regarding the applicability of biodegradable materials are drawn and recommendations for future research are suggested to drive this line of research forward.