As the global health burden of chronic disease increases, end-stage organ failure has become a costly and intractable problem. De novo organ creation is one of the long-term goals of the medical community. One of the promising avenues is that of tissue engineering: the use of biomaterials to create cells, structures, or even whole organs. Tissue engineering has emerged from its nascent stage, with several proof-of-principle trials performed across various tissue types. As tissue engineering moves from the realm of case trials to broader clinical study, three major questions have emerged: (1) Can the production of biological scaffolds be scaled up accordingly to meet current and future demands without generating an unfavorable immune response? (2) Are biological scaffolds plus or minus the inclusion of cells replaced by scar tissue or native functional tissue? (3) Can tissue-engineered organs be grown in children and adolescents given the different immune profiles of children? In this review, we highlight current research in the immunological response to tissue-engineered biomaterials, cells, and whole organs and address the answers to these questions.