Hyaluronic acid (HA) has already been consolidated in the literature as an extremely efficient biopolymer for biomedical applications. In addition to its biodegradability, HA also has excellent biological properties. In the nanofiber form, this polymer can mimic biological tissues, mainly the layers of the skin, and therefore has great potential as structures for the construction of wound dressings. Despite the numerous efforts from the scientific community proposing new dressings, this is an area in constant evolution. A dressing that brings together all the properties of an ideal dressing has not been developed yet. Electrospinning is a simple and versatile technique that correctly aligned with the functional properties of HA can produce multifunctional nanofiber structures capable of promoting skin recover quickly. This review discusses (i) key strategies for successful electrospinning of HA, (ii) main challenges and advances found in the electrospinning process, (iii) the bioactive properties of this polymer in the treatment of wounds, as well as (iv) the results obtained in the last decade by the in vitro and in vivo evaluation of the healing properties of these nanosystems.