Abstract: Quality control chart was driven by Shewhart in 1924, got wide research and applications, plays a important role for the development of world economy. For the classical control charts their parameters, such as sampling interval, sample size and control limit coefficients, are all fixed. Reymold et al （1988） provided the（~X） control charts with variable sampling interval firstly, and then the research field of adaptive control charts has been formed. The researched results of adaptive control charts will be introduced in this paper. Some open problems about adaptive control charts will be given by this paper.