A wide range of perfusable microvessel models have been developed, exploiting advances in microfabrication, microfluidics, biomaterials, stem cell technology, and tissue engineering. These models vary in complexity and physiological relevance, but provide a diverse tool kit for the study of vascular phenomena and methods to vascularize artificial organs. Here we review the state-of-the-art in perfusable microvessel models, summarizing the different fabrication methods and highlighting advantages and limitations.