Microvasculature functions at the tissue and cell level, regulating local mass exchange of oxygen and nutrient-rich blood. While there has been considerable success in the biofabrication of large- and small-vessel replacements, functional microvasculature has been particularly challenging to engineer due to its size and complexity. Recently, three-dimensional bioprinting has expanded the possibilities of fabricating sophisticated microvascular systems by enabling precise spatiotemporal placement of cells and biomaterials based on computer-aided design. However, there are still significant challenges facing the development of printable biomaterials that promote robust formation and controlled 3D organization of microvascular networks. This review provides a thorough examination and critical evaluation of contemporary biomaterials and their specific roles in bioprinting microvasculature. We first provide an overview of bioprinting methods and techniques that enable the fabrication of microvessels. We then offer an in-depth critical analysis on the use of hydrogel bioinks for printing microvascularized constructs within the framework of current bioprinting modalities. We end with a review of recent applications of bioprinted microvasculature for disease modeling, drug testing, and tissue engineering, and conclude with an outlook on the challenges facing the evolution of biomaterials design for bioprinting microvasculature with physiological complexity.