Tissue engineering, which involves the creation of new tissue by the deliberate and controlled stimulation of selected target cells through a systematic combination of molecular and mechanical signals, usually involves the assistance of biomaterials-based structures to deliver these signals and to give shape to the resulting tissue mass. The specifications for these structures, which used to be described as scaffolds but are now more correctly termed templates, have rarely been defined, mainly because this is difficult to do. Primarily, however, these specifications must relate to the need to develop the right microenvironment for the cells to create new tissue and to the need for the interactions between the cells and the template material to be consistent with the demands of the new viable tissues. These features are encompassed by the phenomena that are collectively called biocompatibility. However, the theories and putative mechanisms of conventional biocompatibility (mostly conceived through experiences with implantable medical devices) are inadequate to describe phenomena in tissue-engineering processes. The present author has recently redefined biocompatibility in terms of specific materials- and biology-based pathways; this opinion paper places tissue-engineering biocompatibility mechanisms in the context of these pathways.