Diseases related to vascular malfunction, hyper-vascularization, or lack of vascularization are among the leading causes of morbidity and mortality. Engineered, vascularized tissues as well as angiogenic growth factor-releasing hydrogels could replace defective tissues. Further, treatments and testing of novel vascular therapeutics will benefit significantly from models that allow for the study of vascularized tissues under physiological relevant conditions. Inspired by fibrin, the provisional matrix during wound healing, naturally derived and synthetic hydrogel scaffolds have been developed for vascular engineering. Today, engineers and biologists use commercially available hydrogels to pre-vascularize tissues, to control the delivery of angiogenic growth factors, and to establish vascular diseases models. For clinical translation, pre-vascularized tissue constructs must be sufficiently large and stable to substitute function-relevant tissue defects and integrate with host vascular perfusion. Moreover, the continuous integration of knowhow from basic vascular biology with innovative, tailorable materials and advanced manufacturing technologies is key to achieving near-physiological tissue models and new treatments to control vascularization. For transplantation, engineered tissues must comprise hierarchically organized vascular trees of different caliber and function. The development of novel vascularization-promoting or -inhibiting therapeutics will benefit from physiologically relevant vessel models. In addition, tissue models representing treatment-relevant vascular tissue functions will increase the capacity to screen for therapeutic compounds and will significantly reduce the need for animals for their validation.