The typical displacement pumps are plunger pumps, gear pumps and vane pumps. The first,this paper summarized the problems of plunger pumps which are mechanical noise and fluid noise, lubrication problems of the friction pair and so on. Then it expounded the mechanism and research methods of the problem. Then it summarized the problems and solutions of the gear pumps and the vane pumps which are about the trapped oil, flow pulsation and noise. Do a lot of researches in domestic and foreign Institute, the displacement pumps have been greatly improved in these problems. But the problems such as small volume ratio and high pulsation rate need to be studied and solved. So it is necessary to put forward a new type of displacement pump.