Engineered tissue constructs are inherently limited by their lack of microvascularization. Evidence suggests that combining a scaffold material with cells and their cell-secreted signals instigates tubule formation, and various strategies can be employed to tailor the vascular response. This review focuses on rationally designed materials capable of supporting functional neovessel formation and stabilization. Biomaterial scaffolds and their use as growth factor delivery systems are discussed, as well as other functional enhancement strategies to direct cellular responses for effective formation of a mature vascular network.