This paper reviews reports on three-dimensional mammalian tissue growth in bioreactors and the corresponding mammalian tissue growth requirements. The needs for nutrient and waste removal of several mammalian tissues are reviewed and compared with the environment of many reactors currently in use such as the continuous stirred tank, the hollow fiber, the Couette-Taylor, the airlift, and the rotating-wall reactors developed by NASA. Many studies conclude that oxygen supply appears to be one of the most important factors limiting tissue growth. Various correlations to describe oxygen mass transfer are presented and discussed with the aim to provide some guidance to design, construct, and test reactors for tissue mass culture. To obtain tissue thickness clinically valuable, dimensionless and other types of analysis tend to point out that diffusive transport will have to be matched with an important convection to bring sufficient oxygen molecular flux to the growing cells located within a tissue mass. As learned from solid-state fermentation and hairy root culture, during the growth of large biomass, heterogeneity (i.e., channeling, temperature gradients, non-uniform cell growth, transfer gradients, etc.) can cause some important problems and these should be addressed in tissue engineering as well. Reactors (along with the scaffolds) should be designed to minimize these issues. The role of the uterus, the reactor built by Nature, is examined, and the environment provided to a growing embryo is reported, yielding possible paths for further reactor developments. Finally, the importance of cell seeding methods is also addressed.