Minerals have been important throughout history, but nowadays, their use has increased, as well as their extraction needs. Therefore, due to the growing demand for metals, and both the depletion of high-grade ores and their related environmental concerns, the mining industry has been forced to leave behind the past traditional techniques of metal recovery (use of inorganic acids), and adopt eco-friendlier alternatives, such as the utilization of weaker leaching agents, such as organic acids. Thus, the present review is focused on the use of microbially-produced organic acids as a promising alternative to conventional techniques in the mining industry, with emphasis on the following topics: a) the advantages and disadvantages of the use of organic acids for leaching purposes, b) the main microorganisms studied for the production of these organic acids, c) a summary of the latest reports on bioleaching as well as a comparison of the existent techniques; d) the explanation of leaching mechanisms where organic acids may be involved, to fulfill metal recovery; and, e) interactions between metallic ions and organic acids. The review of the current knowledge regarding the use of organic acids for leaching purposes seeks the visualization of relevant strategies that may be improved for metal-recovery processes, intending to develop circular economy practices that may have the potential to be implemented at an industrial scale.