Diabetic wounds are one of the most common and challenging complications of diabetes. Similar to chronic wounds, diabetic wounds are difficult to treat due to prolonged inflammation, a lack of angiogenesis, abnormal differentiation of new scar tissue, and the occurrence of numerous bacterial infections. Moreover, elevated sugar levels in tissues disrupt the healing process by enhancing inflammatory reactions, disrupting signaling pathways, and leading to the production of abnormal biological structures, which contribute to improper cell differentiation. Traditional dressings, such as bandages, gauze, and semi-occlusive foams, are inadequate for diabetic wounds with high exudation; moreover, frequently changing the dressing can cause secondary irritation. Hence, innovative hydrogel dressings are being developed, which, thanks to their soft polymer matrix, provide an ideal substrate for regenerating tissue. Hydrogels also allow for the introduction and controlled release of growth factors, making them a promising solution for treating diabetic wounds. Recently, researchers have focused on insulin, a hormone secreted by the human body to lower blood sugar levels, due to its interesting characteristics, such as supporting anti-inflammatory and proangiogenic processes and stimulating cell migration and proper proliferation. This review discusses the most important aspects of diabetes and diabetic wounds and traditional and innovative treatment methods, particularly hydrogel dressings used as systems for insulin delivery in response to glucose concentration.