The common occurrence of cardiovascular diseases and the lack of proper autologous tissues prompt and promote the pressing development of tissue-engineered vascular grafts (TEVGs). Current progress on scaffold production, genetically modified cells, and use of nanotechnology-based monitoring has considerably improved the long-term patency of engineered tissue grafts. However, challenges abound in the autologous materials and manipulation of genes and cells for tissue engineering. This review overviews current development in TEVGs and discusses recent improvements in scaffolding techniques and the efficiency of gene-editing tools and their ability to fill the existing gaps in stem cell and regenerative therapies. Current advances in three-dimensional printing approaches for fabrication of engineered tissues are also reviewed together with specific biomaterials for vascular tissues. In addition, the natural and synthetic polymers that hold increasing significance for vascular tissue engineering are highlighted. Both animal models and nanotechnology-based monitoring are proposed for preclinical evaluation of engineered grafts in view of their historical significance in tissue engineering. The ultimate success of tissue regeneration, which is yet to be fully realized, depends on the optimal performance of culture systems, biomaterial constructs, and stem cells in a suitable artificial physiological environment.