Acute skin damage caused by burns or cuts occurs frequently in people’s daily lives. Such wounds are difficult to heal normally and have persistent inflammation. Wound dressings not only improve the speed of wound healing, but also protect and cover the wound well. Hydrogels have the characteristics of good flexibility, high water content, and good biocompatibility, and are widely used in biomedicine and other fields. Common hydrogels are mainly natural hydrogels and synthetic hydrogels. Hydrogels cross-linked using different raw materials and different methods have different performance characteristics. Natural hydrogels prepared using polysaccharides are simple to obtain and have good biocompatibility, but are inferior to synthetic hydrogels in terms of mechanical properties and stability, and a single polysaccharide hydrogel cannot meet the component requirements for wound healing. Therefore, functional composite hydrogels with high mechanical properties, high biocompatibility, and high antibacterial properties are the current research hotspots. In this review, several common polysaccharides for hydrogel synthesis and the synthesis methods of polysaccharide hydrogels are introduced, and functional composite hydrogel dressings from recent years are classified. It is hoped that this can provide useful references for relevant research in this field.