Vascular pathologies are prevalent in a broad spectrum of diseases, necessitating a deeper understanding of vascular biology, particularly in overcoming the oxygen and nutrient diffusion limit in tissue constructs. The evolution of vascularized tissues signifies a convergence of multiple scientific disciplines, encompassing the differentiation of human pluripotent stem cells (hPSCs) into vascular cells, the development of advanced three-dimensional (3D) bioprinting techniques, and the refinement of bioinks. These technologies are instrumental in creating intricate vascular networks essential for tissue viability, especially in thick, complex constructs. This review provides broad perspectives on the past, current state, and advancements in key areas, including the differentiation of hPSCs into specific vascular lineages, the potential and challenges of 3D bioprinting methods, and the role of innovative bioinks mimicking the native extracellular matrix. We also explore the integration of biophysical cues in vascularized tissues in vitro, highlighting their importance in stimulating vessel maturation and functionality. In this review, we aim to synthesize these diverse yet interconnected domains, offering a broad, multidisciplinary perspective on tissue vascularization. Advancements in this field will help address the global organ shortage and transform patient care.