Sustained external supply of oxygen (O) to engineered tissue constructs is important for their survival in the body while angiogenesis is taking place. In the recent years, the trend towards the fabrication of various O-generating materials that can provide prolonged and controlled O source to the large volume tissue constructs resulted in preventing necrosis associated with the lack of O supply. In this review, we explain different methods employed in the fabrication of O-generating materials such as emulsion, microfluidics, solvent casting, freeze drying, electrospraying, gelation, microfluidic and three-dimensional (3D) bioprinting methods. After discussing pros and cons of each method, we review physical, chemical, and biological characterisation techniques used to analyse the resulting product. Finally, the challenges and future directions in the field are discussed.