Reprogramming somatic cells to induced pluripotent stem cells (iPSCs) or direct reprogramming to desired cell types are powerful and new in vitro methods for the study of human disease, cell replacement therapy, and drug development. Both methods to reprogram cells are unconstrained by the ethical and social questions raised by embryonic stem cells. iPSC technology promises to enable personalized autologous cell therapy and has the potential to revolutionize cell replacement therapy and regenerative medicine. Potential applications of iPSC technology are rapidly increasing in ambition from discrete cell replacement applications to the iPSC assisted bioengineering of body organs for personalized autologous body organ transplant. Recent work has demonstrated that the generation of organs from iPSCs is a future possibility. The development of embryonic-like organ structures bioengineered from iPSCs has been achieved, such as an early brain structure (cerebral organoids), bone, optic vesicle-like structures (eye), cardiac muscle tissue (heart), primitive pancreas islet cells, a tooth-like structure (teeth), and functional liver buds (liver). Thus, iPSC technology offers, in the future, the powerful and unique possibility to make body organs for transplantation removing the need for organ donation and immune suppressing drugs. Whilst it is clear that iPSCs are rapidly becoming the lead cell type for research into cell replacement therapy and body organ transplantation strategies in humans, it is not known whether (1) such transplants will stimulate host immune responses; and (2) whether this technology will be capable of the bioengineering of a complete and fully functional human organ. This review will not focus on reprogramming to iPSCs, of which a plethora of reviews can be found, but instead focus on the latest developments in direct reprogramming of cells, the bioengineering of body organs from iPSCs, and an analysis of the immune response induced by iPSC-derived cells and tissues.