The number, the height and the size of concrete dams under construction in China are the biggest ones in the world. Some important problems about concrete dams are discussed in this paper: (1) The key technique for terminating the history of “no dam without crack”.(2) Two kinds of guiding thoughts and two results of practical engineering for application of MgO concrete to dam. (3) Concrete mark based on 90 d or 180 d age is more appropriate for concrete dams than concrete class based on 28 d age . (4) The safety factor for compressive stress for the specially heigh concrete arch dam (higher than 200 m) is some what low in China (5) The equivalent stress in arch dams analysed by the finite element method.