A loss of organs or the destruction of tissue leaves wounds to which organisms and living things react differently. Their response depends on the extent of damage, the functional impairment and the biological potential of the organism. Some can completely regenerate lost body parts or tissues, whereas others react by forming scars in the sense of a tissue repair. Overall, the regenerative capacities of the human body are limited and only a few tissues are fully restored when injured. Dental tissues may suffer severe damage due to various influences such as caries or trauma; however, dental care aims at preserving unharmed structures and, thus, the functionality of the teeth. The dentin-pulp complex, a vital compound tissue that is enclosed by enamel, holds many important functions and is particularly worth protecting. It reacts physiologically to deleterious impacts with an interplay of regenerative and reparative processes to ensure its functionality and facilitate healing. While there were initially no biological treatment options available for the irreversible destruction of dentin or pulp, many promising approaches for endodontic regeneration based on the principles of tissue engineering have been developed in recent years. This review describes the regenerative and reparative processes of the dentin-pulp complex as well as the morphological criteria of possible healing results. Furthermore, it summarizes the current knowledge on tissue engineering of dentin and pulp, and potential future developments in this thriving field.