Tissue engineered grafts show great potential as regenerative implants for diseased or injured tissues within the human body. However, these grafts suffer from poor nutrient perfusion and waste transport, thus decreasing their viability post-transplantation. Graft vascularization is therefore a major area of focus within tissue engineering because biologically relevant conduits for nutrient and oxygen perfusion can improve viability post-implantation. Many researchers utilize microphysiological systems as testing platforms for potential grafts due to an ability to integrate vascular networks as well as biological characteristics such as fluid perfusion, 3D architecture, compartmentalization of tissue-specific materials, and biophysical and biochemical cues. While many methods of vascularizing these systems exist, microvascular self-assembly has great potential for bench-to-clinic translation as it relies on naturally occurring physiological events. In this review, we highlight the past decade of literature and critically discuss the most important and tunable components yielding a self-assembled vascular network on chip: endothelial cell source, tissue-specific supporting cells, biomaterial scaffolds, biochemical cues, and biophysical forces. This article discusses the bioengineered systems of angiogenesis, vasculogenesis, and lymphangiogenesis, and includes a brief overview of multicellular systems. We conclude with future avenues of research to guide the next generation of vascularized microfluidic models and future tissue engineered grafts.