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On a global scale, the demand for mineral products has increased substantially with economic development. Consequently, the mining of mineral resources results in the production and accumulation of a large number of tailings, causing many problems with respect to mining, the environment, and the economy. In the mining process, tailings must be reasonably treated to prevent them from entering the water cycle through rivers. The storage of tailings under water can effectively hinder the chemical reactions that they undergo. Therefore, it is a critical practice to store these substances in ponds or impoundments behind dams. However, tailings dams frequently fail, resulting in the discharge of significant quantities of tailings into the natural environment, thereby causing grievous casualties and serious economic losses. This paper discusses reasons including seepage, foundation failure, overtopping, and earthquake for tailings dam failures and explores failure mechanisms by referring to the available literature. This research has determined that the failure of tailings dams is closely related to the state of the country’s economy. Most of the tailings dam breakages in developed countries occurred decades ago. In recent years, the proportion of tailings dam failures in developing countries has been relatively high. Considering the serious damages caused by tailings dam breakage, it is important to understand the main reasons and mechanisms for their failure. The purpose of this review is to provide a reference for the design and construction to the building of the tailing dams and to reduce the occurrences of their failure.