Wound care challenges healthcare systems worldwide as traditional dressings often fall short in addressing the diverse and complex nature of wound healing. Given conventional treatments limitations, innovative alternatives are urgent. Additive manufacturing (AM) has emerged as a distinct and transformative approach for developing advanced wound dressings, offering unprecedented functionality and customization. Besides exploring the AM processes state-of-the-art, this review comprehensively examines the application of AM to produce cellular-compatible and bioactive, therapeutic agent delivery, patient-centric, and responsive dressings. This review distinguishes itself from the published literature by covering a variety of wound types and by summarizing important data, including used materials, process/technology, printing parameters, and findings from in vitro, ex vivo, and in vivo studies. The prospects of AM in enhancing wound healing outcomes are also analyzed in a translational and cost-effective manner.