Wounds and chronic wounds can be caused by bacterial infections and lead to discomfort in patients. To solve this problem, scientists are working to create modern wound dressings with antibacterial additives, mainly because traditional materials cannot meet the general requirements for complex wounds and cannot promote wound healing. This demand is met by material engineering, through which we can create electrospun wound dressings. Electrospun wound dressings, as well as those based on hydrogels with incorporated antibacterial compounds, can meet these requirements. This manuscript reviews recent materials used as wound dressings, discussing their formation, application, and functionalization. The focus is on presenting dressings based on electrospun materials and hydrogels. In contrast, recent advancements in wound care have highlighted the potential of thermoresponsive hydrogels as dynamic and antibacterial wound dressings. These hydrogels contain adaptable polymers that offer targeted drug delivery and show promise in managing various wound types while addressing bacterial infections. In this way, the article is intended to serve as a compendium of knowledge for researchers, medical practitioners, and biomaterials engineers, providing up-to-date information on the state of the art, possibilities of innovative solutions, and potential challenges in the area of materials used in dressings.