The research on the tie-generative mechanism in network is conductive to explore the factors affecting network evolution and provide theoretical supports and decision-making suggestions for promoting (restraining) the formation (disappearance) of network edges. Based on the analysis of the current situation and development trend of ERGM from 2015 to 2020, this paper presents the research progress and limitations of ERGM. It has made good progress in the fields of network dynamic evolution mechanism, capturing network node heterogeneity, multi-layer network formation mechanism and Research on large (small) scale network formation mechanism. However, it must be admitted that the problems such as extending ERGM to obtain connection weighted information, modeling the heterogeneity of nodes in the network, detecting the multicollinearity that may exist in ERGM, studying the dynamic evolution mechanism of multi-layer network and using ERGM to deal with network missing data have not been well solved, waiting for further exploration.