In the present work an intense bibliographic search is developed, with updated information on the microscopic fundamentals that govern the behavior of flotation operations of chalcopyrite, the main copper mineral in nature. In particular, the effect caused by the presence of pyrite, a non-valuable mineral, but challenging for the operation due to its ability to capture a portion of collector and float, decreasing the quality of the concentrate, is addressed. This manuscript discusses the main chemical and physical mechanisms involved in the phenomena of reagent adsorption on the mineral surface, the impact of pH and type of alkalizing agent, and the effect of pyrite depressants, some already used in the industry and others under investigation. Modern collector reagents are also described, for which, although not yet implemented on an industrial scale, promising results have been obtained in the laboratory, including better copper recovery and selectivity, and even some green reagents present biodegradable properties that generate a better environmental perspective for mineral processing.