Metals are important in many modern industries. Due to the depletion of their natural resource base, it is necessary to adapt, which means developing new and optimizing existing methods of extraction of valuable components from ore materials. Only comprehensive processing of copper metallurgical slags will solve the problem of resource recovery and the creation of low-waste technology, which has great economic, environmental, and social importance. Hydrometallurgical technologies take into account the specific conditions of the system and the physical and chemical properties of metals when developing and selecting the method of extraction. This article provides a review of the current state and prospects of development technologies used for base metal extraction by leaching with the use of inorganic acids and environmentally safe reagents, the methods are conditionally divided into two groups. The listed studies have made a significant contribution to solving the problem of processing metallurgical slags, however, none of the technologies has gone beyond the scope of laboratory and semi-industrial tests. Noted a tendency to reduce the concentrations of leaching agents by certain pre-treatment of raw material, as well as the transition to ubiquitously use "green technologies": such as bioleaching and organic acid leaching. Directions are suggested to solve the problem of rational use of raw materials and increase the sustainability of the future material cycle.