Wound healing is a complex physiological process involving multiple stages, including hemostasis, inflammation, proliferation, and remodeling, which imposes high demands on the functionality and adaptability of wound repair materials. Hydrogels, as a class of novel materials, have become ideal wound dressings due to their excellent biocompatibility, breathability, and conformability. Sodium alginate-based composite hydrogels offer advantages such as readily available raw materials and mild preparation conditions. They can also endow materials with properties including antibacterial, anti-inflammatory, hemostatic, and pro-angiogenic effects, meeting the application requirements for multifunctional and highly efficient wound dressings. As a result, they have attracted considerable attention in the field of wound repair. This article introduces the preparation methods of physically and chemically crosslinked sodium alginate-based composite hydrogels, as well as the drug release mechanisms from these hydrogels. It elaborates on their applications in wound dressings, discusses key challenges including difficulties in large-scale preparation, high barriers to clinical translation, insufficient long-term in vivo stability, and low integration of intelligent functions, and outlines future research directions in terms of large-scale fabrication, regulatory compliance, long-term safety, and intelligent design. This review aims to provide a theoretical basis for the development of novel sodium alginate-based composite hydrogels for wound dressings and to promote their clinical translation and practical application in this field.