Fabricating vascular networks that replicate the hierarchy of native vasculature is one of the leading goals of vascular engineering. This field has mostly focused on dimensional hierarchy so far but will almost certainly need to simultaneously achieve hierarchy of vessel composition (cell types and extracellular matrix), morphology, phenotype and function to successfully recreate the vasculature. a | 3D-printed vascular networks (left and centre images) often have lumen diameters similar to those of arteries or large arterioles, but are lined with only an endothelial monolayer, as is characteristic of capillaries. Endothelialized lumens are shown in the cross-section view, as acquired by confocal microscopy (right image). b | Different fabrication approaches can achieve different lumen diameters, which determine the achievable dimensional hierarchy in engineered vascular networks. c | Different blood-vessel types vary considerably in cellular and matrix composition. Current approaches used for engineering vascular networks can achieve dimensional and compositional hierarchies resembling vascular organization at the capillary and/or arteriole level. Panel a adapted from ref.169, Springer Nature Limited. Panel c adapted with permission from ref.211, The American Physiological Society.