Here we provide literature review on the problem of chronic indolent ulcers and wounds of the skin and subcutaneous tissue, which burden both patients and their families, significantly worsen patients’ quality of life, often cause death, and are associated with significant financial costs. The review notes that the vast majority of chronic ulcers/wounds fall into three main categories: venous ulcers, diabetic ulcers, and decubital ulcers. The smaller fourth group is due to arterial ischemia. The data on the incidence of various categories of chronic ulcers/wounds are provided; modern concepts of their etiopathogenesis are described, including defects of vascularization and oxygen supply to wounds, reduced activity of endothelial progenitor cells, suppression of proliferation and migration of keratinocytes and fibroblasts, dysfunction of HIF1 regulatory cascade, and sharp decrease in the regenerative capacity of the tissue. This review describes conventional treatments for chronic ulcers/wounds based on wound toilet and conservative approaches, as well as modern approaches, including treatment of chronic ulcers/wounds with negative pressure, methods using physical factors and hydrogels, biological therapy using antibodies to tumor necrosis factor alpha, growth factors, and stem cells. We substantiated the need for discovering new methods of prevention and treatment of these pathologies based on the use of cell and gene technologies.