Engineered tissues need a vascular network to supply cells with nutrients and oxygen after implantation. A network that can connect to the vasculature of the patient after implantation can be included during in vitro culture. For optimal integration, this network needs to be highly organized, including venules, capillaries, and arterioles, to supply all of the cells with sufficient nutrients. Owing to the importance of vascularization for the clinical applicability of tissue engineering, many approaches have been investigated to include an organized vascular network in tissue constructs. This review will give an overview of recent efforts, and will propose future perspectives to engineer the optimal, functional vascular network.