Vascular grafts (VG) are medical devices intended to replace the function of a diseased vessel. Current approaches use non-biodegradable materials that struggle to maintain patency under complex hemodynamic conditions. Even with the current advances in tissue engineering and regenerative medicine with the tissue engineered vascular grafts (TEVGs), the cellular response is not yet close to mimicking the biological function of native vessels, and the understanding of the interactions between cells from the blood and the vascular wall with the material in operative conditions is much needed. These interactions change over time after the implantation of the graft. Here we aim to analyze the current knowledge in bio-molecular interactions between blood components, cells and materials that lead either to an early failure or to the stabilization of the vascular graft before the wall regeneration begins.