Melanoma is the most aggressive skin cancer with an increasing number of cases worldwide and curable mostly in its early stage. The improvement in patients’ survival in advanced melanoma has been achieved only recently, due to development of new biological drugs for targeted therapies and immunotherapy. Further progress in the treatment of melanoma is clearly dependent on the better understanding of its complex biology. This review describes the most important molecular mechanisms and genetic events underlying skin melanoma development and progression, depicts the way of action of newly developed drugs and indicates new potential therapeutic targets.