ABSTRACTThe ability to generate new microvessels in desired numbers and at desired locations has been a long‐sought goal in vascular medicine, engineering, and biology. Historically, the need to revascularize ischemic tissues nonsurgically (so‐called therapeutic vascularization) served as the main driving force for the development of new methods of vascular growth. More recently, vascularization of engineered tissues and the generation of vascularized microphysiological systems have provided additional targets for these methods, and have required adaptation of therapeutic vascularization to biomaterial scaffolds and to microscale devices. Three complementary strategies have been investigated to engineer microvasculature: angiogenesis (the sprouting of existing vessels), vasculogenesis (the coalescence of adult or progenitor cells into vessels), and microfluidics (the vascularization of scaffolds that possess the open geometry of microvascular networks). Over the past several decades, vascularization techniques have grown tremendously in sophistication, from the crude implantation of arteries into myocardial tunnels by Vineberg in the 1940s, to the current use of micropatterning techniques to control the exact shape and placement of vessels within a scaffold. This review provides a broad historical view of methods to engineer the microvasculature, and offers a common framework for organizing and analyzing the numerous studies in this area of tissue engineering and regenerative medicine. © 2019 American Physiological Society. Compr Physiol 9:1155‐1212, 2019.