This review summarizes recent trends in the construction of bioartificial vascular replacements, i.e. hybrid grafts containing synthetic polymeric scaffolds and cells. In these advanced replacements, vascular smooth muscle cells (VSMC) should be considered as a physiological component, although it is known that activation of the migration and proliferation of VSMC plays an important role in the onset and development of vascular diseases, and also in restenosis of currently used vascular grafts. Therefore, in novel bioartificial vascular grafts, VSMCs should be kept in quiescent mature contractile phenotype. This can be achieved by (1) appropriate physical and chemical properties of the material, such as its chemical composition, polarity, wettability, surface roughness and topography, electrical charge and conductivity, functionalization with biomolecules and mechanical properties, (2) appropriate cell culture conditions, such as composition of cell culture media and dynamic load, namely cyclic strain, and (3) the presence of a confluent, mature, semipermeable, non-thrombogenic and non-immunogenic endothelial cell (EC) barrier, covering the luminal surface of the graft and separating the VSMCs from the blood. Both VSMCs and ECs can also be differentiated from stem and progenitor cells of various sources. In the case of degradable scaffolds, the material will gradually be removed by the cells and will be replaced by their own new extracellular matrix. Thus, the material component in advanced blood vessel substitutes acts as a temporary scaffold that promotes regeneration of the damaged vascular tissue.