Tissue-engineered vascular grafts (TEVGs) are a promising alternative to treat vascular disease under complex hemodynamic conditions. However, despite efforts from the tissue engineering and regenerative medicine fields, the interactions between the material and the biological and hemodynamic environment are still to be understood, and optimization of the rational design of vascular grafts is an open challenge. This is of special importance as TEVGs not only have to overcome the surgical requirements upon implantation, they also need to withhold the inflammatory response and sustain remodeling of the tissue. This work aims to analyze and evaluate the bio-molecular interactions and hemodynamic phenomena between blood components, cells and materials that have been reported to be related to the failure of the TEVGs during the regeneration process once the initial stages of preimplantation have been resolved, in order to tailor and refine the needed criteria for the optimal design of TEVGs.