Abstract: Copper and cobalt, both strategic metals, play an indispensable role in many fields, such as national infrastructure and defense science and technology. Copper, one of the earliest nonferrous metals discovered, extracted, and applied by humans, teams up with cobalt—a silver-white metal—that serves as a crucial raw material for superalloys, permanent magnets, and chemical industries. The production and consumption of these metals significantly affect the development of national infrastructure, essentially controlling the lifeblood of the national economy. The wide-ranging application of copper and cobalt necessitates an efficient extraction process for these resources. For instance, Congo, Africa, hosts complex copper–cobalt co-associated deposits where the copper–cobalt ratio can reach 3∶1, making it a significant resource. Given the increasing global demand for copper and cobalt, extracting these valuable elements from complex copper–cobalt co-associated ores is of paramount importance. This paper reviews the mineralogical characteristics of these complex resources, including oxidized ores and sulfide ores. It compares and discusses the characteristics of extraction processes such as roasting and leaching. Ultimately, it evaluates the prospects and challenges of extracting copper and cobalt from complex co-associated copper–cobalt deposits. The review reveals that copper–cobalt oxide ores are more compatible with pure wet process treatment, while sulfide ores are better suited for an enhanced leaching process combined with roasting and leaching. The thermodynamic characteristics and kinetic limiting factors of metal extraction from copper–cobalt ores are also compared in this review. In the extraction of the copper–cobalt oxide ore, the mature extraction process is reduction leaching, and different reducing agents show different leaching effects. It is worth noting that there are significant differences in the degree of weathering of copper oxide cobalt ores. Considering Africa’s relatively underdeveloped power facilities and the shortage of chemical reagents, biological leaching and heap leaching present alternative methods for copper oxide cobalt ores. For copper and cobalt sulfide ores, the promising approach for industrial application is a method that combines enrichment, roasting, and leaching. As the copper–cobalt sulfide ore is nearly the only cobalt occurrence mineral, strengthening the phase transformation of copper–cobalt sulfide ore is vital for cobalt extraction. This can be optimized from both thermodynamic and kinetic perspectives. The aim of this paper is to provide some references for the efficient and reasonable collaborative extraction and utilization of copper–cobalt resources.