Bioreactors, i.e. devices in which biochemical reactions are carried out, are the core components of a new generation of biomedical devices, which replace or support the function of failing human organs by using cultured living cells (bio-artificial organs). This chapter presents the fundamentals of bioreactor engineering: enzymatic reactions, cell cultures and tissue engineering are considered and presented on the basis of mass and energy transport equations and reaction kinetics. A significant part of the chapter is devoted to the kinetics of reactions catalyzed by enzymes, both free and entrapped in microcapsules or hollow fibres. Cell growth kinetics with immobilized cells are also described and two interesting models are presented for evaluating the anoxic zones in alginate gel beads entrapping hepatocytes or for designing a hollow fibre bioreactor with cells immobilized on the membrane. The chapter is completed by a short overview of bioreactors for tissue engineering.