The progress, problem and prospect of long and medium-term earthquake prediction research are outlined. The research history can be divided into two stages: definitive prediction and probability prediction. There are many problems in the existing models and methods such as earthquake recurrence model, analysis of non-definition, interaction between faults and short of information. So, in the future, the main research fields of long and medium-term earthquake prediction are as follows:①Establish earthquake recurrence model,②Establish a generic recurrence interval distribution model appropriate for intraplate earthquake,③Application of the quantitative research date of active fault,④Analysis of non-definition,⑤Interaction between faults and its effects, and⑥Application of multidisciplinary approach.