The great variety of wounds and the lack of an effective universal treatment method has resulted in high demand for modern treatment strategies. Traditional approaches are often ineffective on a variety of chronic wounds, such as venous ulcers or the diabetic foot ulcer. There is strong evidence that naturally derived bioactive compounds have pro-healing properties, raising a great interest in their potential use for wound healing. Plant-derived compounds, such as curcumin and essential oils, are widely used to modify materials applied as wound dressings. Moreover, dressing materials are more often enriched with vitamins (e.g., L-ascorbic acid, tocopherol) and drugs (e.g., antibiotics, inhibitors of proteases) to improve the skin healing rate. Biomaterials loaded with the above-mentioned molecules show better biocompatibility and are basically characterized by better biological properties, ensuring faster tissue repair process. The main emphasis of the presented review is put on the novel findings concerning modern pro-healing wound dressings that have contributed to the development of regenerative medicine. The article briefly describes the synthesis and modifications of biomaterials with bioactive compounds (including curcumin, essential oils, vitamins) to improve their pro-healing properties. The paper also summarizes biological effects of the novel wound dressings on the enhancement of skin regeneration. The current review was prepared based on the scientific contributions in the PubMed database (supported with Google Scholar searching) over the past 5 years using relevant keywords. Scientific reports on the modification of biomaterials using curcumin, vitamins, and essential oils were mainly considered.