Tissue engineering aims at the creation of living neo-tissues identical or close to their native human counterparts. As basis of this approach, temporary biodegradable supporter matrices are fabricated in the shape of a desired construct, which promote tissue strength and provide functionality until sufficient neo-tissue is formed. Besides fully synthetic polymer-based scaffolds, decellularized biological tissue of xenogenic or homogenic origin can be used. In a second step, these scaffolds are seeded with autologous cells attaching to the scaffold microstructure. In order to promote neo-tissue formation and maturation, the seeded scaffolds are exposed to different forms of stimulation. In cardiovascular tissue engineering, this "conditioning" can be achieved via culture media and biomimetic in vitro exposure, e.g., using flow bioreactors. This aims at adequate cellular differentiation, proliferation, and extracellular matrix production to form a living tissue called the construct. These living autologous constructs, such as heart valves or vascular grafts, are created in vitro, comprising a viable interstitium with repair and remodeling capabilities already prior to implantation. In situ further in vivo remodeling is intended to recapitulate physiological vascular architecture and function. The remodeling mechanisms were shown to be dominated by monocytic infiltration and chemotactic host-cell attraction leading into a multifaceted inflammatory process and neo-tissue formation. Key molecules of these processes can be integrated into the scaffold matrix to direct cell and tissue fate in vivo.