Fabrication of vascular networks within engineered tissue remains one of the greatest challenges facing the fields of biomaterials and tissue engineering. Historically, the structural complexity of vascular networks has limited their fabrication in tissues engineered in vitro. Recently, however, key advances have been made in constructing fluidic networks within biomaterials, suggesting a strategy for fabricating the architecture of the vasculature. These techniques build on emerging technologies within the microfluidics community as well as on 3D printing. The freeform fabrication capabilities of 3D printing are allowing investigators to fabricate fluidic networks with complex architecture inside biomaterial matrices. In this review, we examine the most exciting 3D printing-based techniques in this area. We also discuss opportunities for using these techniques to address open questions in vascular biology and biophysics, as well as for engineering therapeutic tissue substitutes in vitro.