Coal has remained the primary component of China’s energy structure, and high-intensity extraction has continued in the central and western coal-producing regions of China. In contrast to the abundant coal resources, water resources have become extremely scarce in these regions, creating a conflict between coal resource extraction and water resource conservation. The coal mine underground reservoir (CMUR), as a typical technology for combined coal and water extraction and water-preserving coal mining, has been applied in numerous mines in central and western China. This effectively alleviates water resource shortages and achieves the goal of water resource conservation. The CMURs utilizes the goaf created by longwall mining as the water storage space. The reservoir dam structure comprises coal pillars, which serve as protective coal pillars in the mining area, and artificial dam structures that filled the gaps between these coal pillars. The stability of the dam structure under the complex stress effects of hydraulic coupling has been identified as the key to maintaining the safe operation of the CMUR. The mechanical properties, stress field, fracture field, and seepage field (“three fields”) change mechanisms, as well as the research results on size optimization of coal pillar dams and artificial dams in CMURs, were systematically reviewed. The core content included the instability and failure mechanisms of dam structures under the comprehensive coupling effects of factors such as dry–wet cycles of mine water, long-term immersion, chemical effects of high-salinity water, dynamic and static loads, and cyclic loads. This paper is considered to have certain reference value for the study of the stability of dam structures in CMURs and to provide some guidance for the safe operation of CMURs.