Biomaterials are pivotal in supporting and guiding vascularization for therapeutic applications. To design effective, bioactive biomaterials, understanding the cellular and molecular processes involved in angiogenesis and vasculogenesis is crucial. Biomaterial platforms can replicate the interactions between cells, the ECM, and the signaling molecules that trigger blood vessel formation. Hydrogels, with their soft and hydrated properties resembling natural tissues, are widely utilized; particularly synthetic hydrogels, known for their bio-inertness and precise control over cell–material interactions, are utilized. Naturally derived and synthetic hydrogel bases are tailored with specific mechanical properties, controlled for biodegradation, and enhanced for cell adhesion, appropriate biochemical signaling, and architectural features that facilitate the assembly and tubulogenesis of vascular cells. This comprehensive review showcases the latest advancements in hydrogel materials and innovative design modifications aimed at effectively guiding and supporting vascularization processes. Furthermore, by leveraging this knowledge, researchers can advance biomaterial design, which will enable precise support and guidance of vascularization processes and ultimately enhance tissue functionality and therapeutic outcomes.