Wound closure represents a primary goal in the treatment of very deep and/or large wounds, for which the mortality rate is particularly high. However, the spontaneous healing of adult skin eventually results in the formation of epithelialized scar and scar contracture (repair), which might distort the tissues and cause lifelong deformities and disabilities. This clinical evidence suggests that wound closure attained by means of skin regeneration, instead of repair, should be the true goal of burn wound management. The traditional concept of temporary wound dressings, able to stimulate skin healing by repair, is thus being increasingly replaced by the idea of temporary scaffolds, or regenerative templates, able to promote healing by regeneration. As wound dressings, polymeric hydrogels provide an ideal moisture environment for healing while protecting the wound, with the additional advantage of being comfortable to the patient, due to their cooling effect and non-adhesiveness to the wound tissue. More importantly, recent advances in regenerative medicine demonstrate that bioactive hydrogels can be properly designed to induce at least partial skin regeneration in vivo. The aim of this review is to provide a concise insight on the key properties of hydrogels for skin healing and regeneration, particularly highlighting the emerging role of hydrogels as next generation skin substitutes for the treatment of full-thickness burns.