Abstract: Accurate and reliable prediction of mining subsidence is not only the important basis for the optimal design of underground work face and the evaluation of surface mining damage, but also for the design of land reclamation and ecological reconstruction, and the reasonable evaluation of the stability and suitability for old mining surface subsidence areas.With the progress of theoretical study and practice, the research hotspot has been changed from the final static prediction to the progressive surface subsidence with time.Once less than 30 mm of accumulative surface subsidence occurs in six months in the weakening period, the traditional surface movement ends, which indicates stabilized surface.However, under the action of the long-term load for overburden rock strata, the residual surface subsidence will continue with the compactions of broken roof rocks, bed separations, and cracks in overburden, considerable attention has been devoted to the subject of the residual subsidence prediction.Based on the law of mining surface movement, the entire process of mining subsidence is divided into two stages.The first stage is the progressive subsidence including initial, active and weakening periods, and the second stage is named residual surface subsidence after the weakening period.For the first stage, the advances and defects are analyzed and the principle of progressive mining subsidence, which is a combined time function and probabilistic integral method, is given.The spatio-temporal datum of progressive prediction for multi-working face mining is proposed.It must be noted that the progressive prediction and comparison are not sufficient only considering the time without underground mining.The final mining subsidence is a special case of progressive subsidence under the condition of time infinity.That is to say that this method is suitable to predict the delayed subsidence at the end of the weakening period but not suitable to predict the residual surface subsidence after the weakening period.For the second stage, based on the continuity of surface subsidence at the end of the weakening period and the residual subsidence in the first year, and a linear monotonic decrease in the residual subsidence factor because of the smaller residual subsidence, the expressions of duration and annual residual subsidence factor are achieved.The quantitative calculation of the duration and annual residual surface subsidence factor can be carried out under the given geo-mining conditions.From the point of view of the current status for the entire process of mining subsidence prediction, the problems of computational element length, irregular working face, and the mining effect of vicinity working faces for progressive surface subsidence are discussed.The existing problems for residual surface subsidence related to compacting factor for broken rocks, damaged and crushed effect of coal pillars, calculating area for prediction, reliability and uncertainty for prediction, etc.are also proposed and discussed.All those problems can be consulted and remain to be solved in the future.