Social network (SN) has become a popular research field in both academia and industry. However, most of the current studies in this field mainly focuses on a single SN. Obviously, the integration of SNs, termed as social network integration (SNI), provides more sufficient user behavior data and more complete network structure for the studies on SN such as social computing. Additionally, SNI is more effective in excavating and understanding human society through SNs. Thus, it has significant theoretical and practical value to explore problems in SNI. Correlating users refer to the user accounts belonging to the same individual in different SNs. Since users naturally bridge the SNs, correlating user mining problem is the fundamental task of SNI, hence having attracted extensive attention. Due to the unfavorable characteristics of SN, correlating user mining problem is still a hard nut to crack. In this paper, the difficulties in the correlating user mining task are analyzed, and the methods addressing this issue are summarized. Finally, some potential future research work is suggested.