The vasculature is an essential component of the circulatory system that plays a vital role in the development, homeostasis, and disease of various organs in the human body. The ability to emulate the architecture and transport function of blood vessels in the integrated context of their associated organs represents an important requirement for studying a wide range of physiological processes. Traditional in vitro models of the vasculature, however, largely fail to offer such capabilities. Here we combine microfluidic three-dimensional (3D) cell culture with the principle of vasculogenic self-assembly to engineer perfusable 3D microvascular beds in vitro. Our system is created in a micropatterned hydrogel construct housed in an elastomeric microdevice that enables coculture of primary human vascular endothelial cells and fibroblasts to achieve de novo formation, anastomosis, and controlled perfusion of 3D vascular networks. An open-top chamber design adopted in this hybrid platform also makes it possible to integrate the microengineered 3D vasculature with other cell types to recapitulate organ-specific cellular heterogeneity and structural organization of vascularized human tissues. Using these capabilities, we developed stem cell-derived microphysiological models of vascularized human adipose tissue and the blood-retinal barrier. Our approach was also leveraged to construct a 3D organotypic model of vascularized human lung adenocarcinoma as a high-content drug screening platform to simulate intravascular delivery, tumor-killing effects, and vascular toxicity of a clinical chemotherapeutic agent. Furthermore, we demonstrated the potential of our platform for applications in nanomedicine by creating microengineered models of vascular inflammation to evaluate a nanoengineered drug delivery system based on active targeting liposomal nanocarriers. These results represent a significant improvement in our ability to model the complexity of native human tissues and may provide a basis for developing predictive preclinical models for biopharmaceutical applications.