Three-dimensional bioprinting has emerged as a groundbreaking approach for fabricating living tissues and organ analogs with spatial and structural fidelity. By integrating biomaterials, living cells, and bioactive molecules through computer-aided design, bioprinting allows for the construction of biologically relevant architectures that closely mimic native tissue organization. Despite significant progress, one of the most formidable barriers to the clinical translation of engineered tissues remains the challenge of vascularization. The successful integration of engineered constructs into host tissue in vivo critically depends on the formation of functional vasculature. The human vascular system is a highly organized, multiscale network composed of a variety of blood vessels, each with distinct morphological and physiological roles. Reproducing the multiscale architecture of the vascular system, ranging from large arteries to microscopic capillaries, is therefore fundamental to the development of functional tissue and organ replacements. This review highlights the central role of vascularization in tissue engineering, discussing current strategies, emerging technologies, and future directions aimed at replicating the intricate multiscale vasculature necessary to achieve the functional and morphological fidelity of engineered tissues.