Blood vessels are fundamental to animal life and have critical roles in many diseases, such as stroke, myocardial infarction and diabetes. The vasculature is formed by endothelial cells that line the vessel and are covered with mural cells, specifically pericytes in smaller vessels and vascular smooth muscle cells (vSMCs) in larger-diameter vessels. Both endothelial cells and mural cells are essential for proper blood vessel function and can be derived from human pluripotent stem cells (hPSCs). Here, we describe a protocol to generate self-organizing 3D human blood vessel organoids from hPSCs that exhibit morphological, functional and molecular features of human microvasculature. These organoids are differentiated via mesoderm induction of hPSC aggregates and subsequent differentiation into endothelial networks and pericytes in a 3D collagen I-Matrigel matrix. Blood vessels form within 2-3 weeks and can be further grown in scalable suspension culture. Importantly, in vitro-differentiated human blood vessel organoids transplanted into immunocompromised mice gain access to the mouse circulation and specify into functional arteries, arterioles and veins.