Vascular tissue engineering has the potential to make a significant impact on the treatment of a wide variety of medical conditions, including providing in vitro generated vascularized tissue and organ constructs for transplantation. Since the first report on the construction of a biological blood vessel, significant research and technological advances have led to the generation of clinically relevant large and small diameter tissue engineered vascular grafts (TEVGs). However, developing a biocompatible blood-contacting surface is still a major challenge. Researchers are using biomimicry to generate functional vascular grafts and vascular networks. A multi-disciplinary approach is being used that includes biomaterials, cells, pro-angiogenic factors and microfabrication technologies. Techniques to achieve spatiotemporal control of vascularization include use of topographical engineering and controlled-release of growth/pro-angiogenic factors. Use of decellularized natural scaffolds has gained popularity for engineering complex vascularized organs for potential clinical use. Pre-vascularization of constructs prior to implantation has also been shown to enhance its anastomosis after implantation. Host-implant anastomosis is a phenomenon that is still not fully understood. However, it will be a critical factor in determining the in vivo success of a TEVGs or bioengineered organ. Many clinical studies have been conducted using TEVGs, but vascularized tissue/organ constructs are still in the research & development stage. In addition to technical challenges, there are commercialization and regulatory challenges that need to be addressed. In this review we examine recent advances in the field of vascular tissue engineering, with a focus on technology trends, challenges and potential clinical applications.