Tissue engineering is currently limited by the inability to adequately vascularize tissues in vitro or in vivo. Issues of nutrient perfusion and mass transport limitations, especially oxygen diffusion, restrict construct development to smaller than clinically relevant dimensions and limit the ability for in vivo integration. There is much interest in the field as researchers have undertaken a variety of approaches to vascularization, including material functionalization, scaffold design, microfabrication, bioreactor development, endothelial cell seeding, modular assembly, and in vivo systems. Efforts to model and measure oxygen diffusion and consumption within these engineered tissues have sought to quantitatively assess and improve these design strategies. This review assesses the current state of the field by outlining the prevailing approaches taken toward producing vascularized tissues and highlighting their strengths and weaknesses.