In human vascular anatomy, blood flows from the heart to organs and tissues through a hierarchical vascular tree, comprising large arteries that branch into arterioles and further into capillaries, where gas and nutrient exchange occur. Engineering a complete, integrated vascular hierarchy with vessels large enough to suture, strong enough to withstand hemodynamic forces, and a branching structure to permit immediate perfusion of a fluidic circuit across scales would be transformative for regenerative medicine (RM), enabling the translation of engineered tissues of clinically relevant size, and perhaps whole organs. How close are we to solving this biological plumbing problem? In this review, we highlight advances in engineered vasculature at individual scales and focus on recent strategies to integrate across scales.