With the in-depth understanding of bone regeneration mechanisms and the development of bone tissue engineering, a variety of scaffold carrier materials with desirable physicochemical properties and biological functions have recently emerged in the field of bone regeneration. Hydrogels are being increasingly used in the field of bone regeneration and tissue engineering because of their biocompatibility, unique swelling properties, and relative ease of fabrication. Hydrogel drug delivery systems comprise cells, cytokines, an extracellular matrix, and small molecule nucleotides, which have different properties depending on their chemical or physical cross-linking. Additionally, hydrogels can be designed for different types of drug delivery for specific applications. In this paper, we summarize recent research in the field of bone regeneration using hydrogels as delivery carriers, detail the application of hydrogels in bone defect diseases and their mechanisms, and discuss future research directions of hydrogel drug delivery systems in bone tissue engineering.