End-stage organ failure is a key challenge for the medical community because of the ageing population and the severe shortage of suitable donor organs available. Equally, injuries to or congenital absence of complex tissues such as the trachea, oesophagus, or skeletal muscle have few therapeutic options. A new approach to treatment involves the use of three-dimensional biological scaffolds made of allogeneic or xenogeneic extracellular matrix derived from non-autologous sources. These scaffolds can act as an inductive template for functional tissue and organ reconstruction after recellularisation with autologous stem cells or differentiated cells. Such an approach has been used successfully for the repair and reconstruction of several complex tissues such as trachea, oesophagus, and skeletal muscle in animal models and human beings, and, guided by appropriate scientific and ethical oversight, could serve as a platform for the engineering of whole organs and other tissues.