Bone tissue engineering (BTE) has become a hopeful potential treatment strategy for large bone defects, including bone tumors, trauma, and extensive fractures, where the self-healing property of bone cannot repair the defect. Bone tissue engineering is composed of three main elements: progenitor/stem cells, scaffold, and growth factors/biochemical cues. Among the various biomaterial scaffolds, hydrogels are broadly used in bone tissue engineering owing to their biocompatibility, controllable mechanical characteristics, osteoconductive, and osteoinductive properties. During bone tissue engineering, angiogenesis plays a central role in the failure or success of bone reconstruction via discarding wastes and providing oxygen, minerals, nutrients, and growth factors to the injured microenvironment. This review presents an overview of bone tissue engineering and its requirements, hydrogel structure and characterization, the applications of hydrogels in bone regeneration, and the promising roles of hydrogels in bone angiogenesis during bone tissue engineering.