Effective wound treatment has become one of the most important challenges for healthcare as it continues to be one of the leading causes of death worldwide. Therefore, wound care technologies significantly evolved in order to provide a holistic approach based on various designs of functional wound dressings. Among them, hydrogels have been widely used for wound treatment due to their biocompatibility and similarity to the extracellular matrix. The hydrogel formula offers the control of an optimal wound moisture level due to its ability to absorb excess fluid from the wound or release moisture as needed. Additionally, hydrogels can be successfully integrated with a plethora of biologically active components (e.g., nanoparticles, pharmaceuticals, natural extracts, peptides), thus enhancing the performance of resulting composite hydrogels in wound healing applications. In this review, the-state-of-the-art discoveries related to stimuli-responsive hydrogel-based dressings have been summarized, taking into account their antimicrobial, anti-inflammatory, antioxidant, and hemostatic properties, as well as other effects (e.g., re-epithelialization, vascularization, and restoration of the tissue) resulting from their use.