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Human induced pluripotent stem cell (iPSC)-derived brain organoids have emerged as powerful three-dimensional (3D) platforms for modeling human neurodevelopment and neurological disorders. However, the absence of a functional vascular network remains a critical limitation, restricting oxygen and nutrient delivery, impairing metabolic stability, and constraining long-term maturation. Conventional extracellular matrix (ECM) mimetics, such as Matrigel and other static synthetic hydrogels, provide biochemical support but fail to recapitulate the dynamic remodeling that characterizes the developing neurovascular niche. Recent advances in stimuli-responsive hydrogels offer spatiotemporal control over matrix stiffness, degradability, viscoelasticity, and biochemical cue presentation. In this review, we discuss dynamic hydrogel systems within a structure–property–function framework, highlighting how network chemistry and architecture may regulate endothelial sprouting, lumen formation, vascular stabilization, and neurovascular unit maturation in vascularized brain organoid models, based on evidence from both organoid studies and related biomaterial or vascular systems. Photoresponsive, enzyme-cleavable, thermo-responsive, supramolecular, bio-orthogonal click-based, and bioprinted platforms are discussed with emphasis on mechanotransduction, angiocrine signaling, and barrier specialization. Functional outcomes, including trans-endothelial electrical resistance, selective permeability, transporter expression, electrophysiological integration, and sustained perfusion, are discussed alongside translational challenges such as cytocompatibility, oxidative stress, scalability, and regulatory feasibility. Collectively, dynamic hydrogels provide a versatile biomaterial strategy for improving vascularization and aspects of functional maturation in brain organoid models with enhanced physiological relevance. Ultimately, stimuli-responsive hydrogel systems may serve as enabling platforms for engineering vascularized brain organoids and advancing human-relevant neurovascular disease modeling.