The microvasculature is an extensive, heterogeneous, and complex system that plays a critical role in human physiology and disease. It nourishes almost all living human cells and maintains a local microenvironment that is vital for tissue and organ function. Operating under a state of continuous flow, with an intricate architecture despite its small caliber, and subject to a multitude of biophysical and biochemical stimuli, the microvasculature can be a complex subject to study in the laboratory setting. Engineered microvessels provide an ideal platform that recapitulates essential elements of in vivo physiology and allows study of the microvasculature in a precise and reproducible way. Here, we review relevant structural and functional vascular biology, discuss different methods to engineer microvessels, and explore the applications of this exciting tool for the study of human disease.