This work reviews the tremendous development in the field of vascular graft tissue engineering driven by a clear and increasing clinical need for functional vascular replacements able to grow and remodel. The different strategies to tissue engineer blood vessels are presented, from the classical approach of a living implant generated in vitro by conditioning a cell-seeded scaffold to remarkable paradigm shifts either i) toward a completely biology-driven strategy (scaffold-free approaches) or ii) the opposite tendency of cell-free scaffolds aiming at eliciting the host reaction for in situ tissue engineering. In the scaffold-based approaches emphasis is given to the material choice.