To date, there is increasing clinical need for vascular substitutes due to accidents, malformations, and ischemic diseases. Over the years, many approaches have been developed to solve this problem, starting from autologous native vessels to artificial vascular grafts; unfortunately, none of these have provided the perfect vascular substitute. All have been burdened by various complications, including infection, thrombogenicity, calcification, foreign body reaction, lack of growth potential, late stenosis and occlusion from intimal hyperplasia, and pseudoaneurysm formation. In the last few years, vascular tissue engineering has emerged as one of the most promising approaches for producing mechanically competent vascular substitutes. Nanotechnologies have contributed their part, allowing extraordinarily biostable and biocompatible materials to be developed. Specifically, the use of electrospinning to manufacture conduits able to guarantee a stable flow of biological fluids and guide the formation of a new vessel has revolutionized the concept of the vascular substitute. The electrospinning technique allows extracellular matrix (ECM) to be mimicked with high fidelity, reproducing its porosity and complexity, and providing an environment suitable for cell growth. In the future, a better knowledge of ECM and the manufacture of new materials will allow us to “create” functional biological vessels - the base required to develop organ substitutes and eventually solve the problem of organ failure.