A proper supply of nutrients to cells in engineered tissues is paramount for an optimal development and survival of these tissues. However, especially in tissues with clinically relevant sizes, the mass transport of nutrients into the tissue is often insufficient to sustain all the cells within the tissue. This is not only the case during in vitro culture. After implantation of an engineered tissue, a vascular network is not directly established. Therefore, the mass transport of nutrients is also critical during the initial period after implantation. This review introduces the basics of mass transport, leading to the conclusion that three main concepts can be used to increase nutrient supply in tissue engineering. These are; increasing the overall diffusion coefficient, decreasing the diffusion distance, or increasing convective transport. Based on these concepts, the main strategies that have been developed to enhance the supply of nutrients to cells in engineered tissues will be discussed.