The idea to create the concept of cardiovascular "tissue engineering" is based on the recognition that until then all known allogeneic/xenogeneic biological or alloplastic implant materials were associated with shortcomings, which led to graft deterioration, degradation and finally destruction. Thus, it aims to develop viable cardiovascular structures, e.g. heart valves, myocardium or blood vessels, which ideally demonstrate mechanisms of remodeling and self-repair, a high microbiological resistance, complete immunological integrity and a functional endothelial cell layer to guarantee physiological hemostasis. In our current review we aim to identify basic limitations of previous concepts, explain why the use of decellularized matrices was a logical consequence and which limitations still exist.