ABSTRACT This Review explores the rapidly evolving field of bioengineered vasculature, a key area of focus in tissue engineering and regenerative medicine. The broad relevance of this topic is attributed to its impacts on a wide range of biological processes, enabling studies in tissue development, fundamental biology and drug discovery, and the applications in tissue engineering and regenerative medicine. We outline the design criteria for bioengineered vasculature and the methodologies for constructing these systems by self-assembly and in microfluidics, organs-on-a-chip and macroscale tubular systems that often rely on biofabrication approaches such as 3D printing. We discuss existing challenges in developing functional vasculature that closely mirrors its native equivalent, including achieving hierarchical branching with organ and vessel-specific endothelial and supporting cells, providing perusable vasculature within organoids and scaling the systems for implantation and direct vascular anastomosis.