The limited availability of transplantable organs hinders the success of patient treatment through organ transplantation. In addition, there are challenges with immune rejection and the risk of disease transmission when receiving organs from other individuals. Tissue engineering aims to overcome these challenges by generating functional three-dimensional (3D) tissue constructs. When developing tissues or organs of a particular shape, structure, and size as determined by the specific needs of the therapeutic intervention, a tissue specific oxygen supply to all parts of the tissue construct is an utmost requirement. Moreover, the lack of a functional vasculature in engineered tissues decreases cell survival upon implantation in the body. Oxygen-generating materials can alleviate this challenge in engineered tissue constructs by providing oxygen in a sustained and controlled manner. Oxygen-generating materials can be incorporated into 3D scaffolds allowing the cells to receive and utilize oxygen efficiently. In this review, we present an overview of the use of oxygen-generating materials in various tissue engineering applications in an organ specific manner as well as their potential use in the clinic.