The most important strategy in tissue engineering is combining scaffolds with living cells to form tissue-engineered compositions (TECs) to promote the repair and regeneration of tissues. Such scaffolds are expected to support cell colonization, migration, growth, and differentiation, and to guide the development of the required tissues. TECs stored at ambient temperature require expensive human involvement to satisfy metabolic demands and can potentially be infected and biologically altered. For the commercialization and large-scale clinical applications of tissue engineering, long-term and stable methods that preserve TECs that contain living cells and maintain their adhesion to scaffolds are required. Cryopreservation can be achieved by vitrification, which can improve the post-rewarming viability of cells and reduce intra- and intercellular ice formation. The present paper reviews the literature and clarifies the basic technological advances of vitreous cryopreservation of TECs. The specific requirements for the vitreous cryopreservation of TECs are defined. The physicochemical basis for vitreous cryopreservation, cryoprotectant properties, and model studies are emphasized. Examples of TEC vitrification are given. It is concluded that vitrification is a promising method for the preservation of TECs and is likely to lead to the off-the-shelf availability of TECs for tissue repair.