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Developing vascular cells have been shown to self-organize into unique structures in both two and three dimensions. Depending on the conditions, these cells may develop micropatterns with spatial segregation of different cell types in 2D or develop into perfusable vascular vessels in 3D. This self-organization arises from the interplay of motility, proliferation, differentiation, and cellular signaling; with the relative importance of these factors remaining unclear. In this dissertation, I report the development and use of a computational model to explore how motility, proliferation, and differentiation rates affect the emergence of micropatterns from differentiating vascular cells in a 2D in silico environment. Later, I explore the in vitro vascular development, via a microfluidic platform, of vascular networks that are functional, perfusable, and stable for more than two months. Firstly, I developed a stochastic on-lattice population-based model to study the emergence of vascular patterns from a starting distribution of stem cell induced vascular progenitor cells capable of differentiating into both endothelial cells and smooth muscle cells that are motile and proliferative. Our model yielded patterns that were qualitatively and quantitatively consistent with our experimental observations, for physiologically reasonable parameters. Our results suggest that, for such parameter values, it is the post-differentiation motility and proliferation rates that drive the formation of vascular patterns more than differentiation alone. This was shown to be true even when higher order effects like density dependent adhesions and paracrine signaling were considered. Secondly, microfluidic devices and organ-on-a-chip models have become good solutions for studying 3D cell cultures that more closely mimic physiologically relevant lengths and timescales. These devices allow for the incorporation of height into cultures by suspending cells in extracellular matrices, such as fibrin, that more closely mimic in vivo microenvironments. Here I also report the use of endothelial cells in culture with mural cells, smooth muscle cells and pericyte cell cultures, as ideal conditions for the successful development of perfusable vasculature within a three-channel microfluidic device. We found the use of these cells, in tri-culture, to lead to the development of physiologically narrow vessels that were functional and perfusable for more than two months. These findings hint at methods that could be employed for directing specific micropatterns or 3D structures that focus on controlling the motility and proliferation rates of differentiating stem cells. Furthermore, these studies aim to advance the field of organoid development, by providing a reliable method for developing fully vascularized organoids and organs that are stable for long time-scales.