Wound healing involves a complex cascade of cellular, molecular, and biochemical responses and signaling processes. It consists of successive interrelated phases, the duration of which depends on a multitude of factors. Wound treatment is a major healthcare issue that can be resolved by the development of effective and affordable wound dressings based on natural materials and biologically active substances. The proper use of modern wound dressings can significantly accelerate wound healing with minimum scar mark. Sulfated polysaccharides from seaweeds, with their unique structures and biological properties, as well as with a high potential to be used in various wound treatment methods, now undoubtedly play a major role in innovative biotechnologies of modern natural interactive dressings. These natural biopolymers are a novel and promising biologically active source for designing wound dressings based on alginates, fucoidans, carrageenans, and ulvans, which serve as active and effective therapeutic tools. The goal of this review is to summarize available information about the modern wound dressing technologies based on seaweed-derived polysaccharides, including those successfully implemented in commercial products, with a focus on promising and innovative designs. Future perspectives for the use of marine-derived biopolymers necessitate summarizing and analyzing results of numerous experiments and clinical trial data, developing a scientifically substantiated approach to wound treatment, and suggesting relevant practical recommendations.