Generating perfusable 3D microvessels in vitro is an important goal for tissue engineering, as well as for reliable modelling of blood vessel function. To date, in vitro blood vessel models have not been able to accurately reproduce the dynamics and responses of endothelial cells to grow perfusable and functional 3D vascular networks. Here we describe a microfluidic-based platform whereby we model natural cellular programs found during normal development and angiogenesis to form perfusable networks of intact 3D microvessels as well as tumor vasculatures based on the spatially controlled co-culture of endothelial cells with stromal fibroblasts, pericytes or cancer cells. The microvessels possess the characteristic morphological and biochemical markers of in vivo blood vessels, and exhibit strong barrier function and long-term stability. An open, unobstructed microvasculature allows the delivery of nutrients, chemical compounds, biomolecules and cell suspensions, as well as flow-induced mechanical stimuli into the luminal space of the endothelium, and exhibits faithful responses to physiological shear stress as demonstrated by cytoskeleton rearrangement and increased nitric oxide synthesis. This simple and versatile platform provides a wide range of applications in vascular physiology studies as well as in developing vascularized organ-on-a-chip and human disease models for pharmaceutical screening.