Vascularization is one of the great challenges that tissue engineering faces in order to achieve sizeable tissue and organ substitutes that contain living cells. There are instances, such as skin replacement, in which a tissue-engineered substitute does not absolutely need a preexisting vascularization. However, tissue or organ substitutes in which any dimension, such as thickness, exceeds 400 μm need to be vascularized to ensure cellular survival. Consistent with the wide spectrum of approaches to tissue engineering itself, which vary from acellular synthetic biomaterials to purely biological living constructs, approaches to tissue-engineered vascularization cover numerous techniques. Those techniques range from micropatterns engineered in biomaterials to microvascular networks created by endothelial cells. In this review, we strive to provide a critical overview of the elements that must be considered in the pursuit of this goal and the major approaches that are investigated in hopes of achieving it.