ECHO progress was defined to depict the rotordynamic pump theory development. Experience (E) era for pumps lasted nearly one and a half hundred years before the Industrial Revolution due to the low rotation speed of motor and undeveloped manufacture ability. Classic (C) theory referring to quasi-static performance as well as the items those were not able to be steadily resolved under the level were briefly and sophisticated outlined. Since 1962, flow instabilities and the dynamic responses had come into main attention with the development of the modern technologies such as ballistic missile, rocket and space shuttle main engine, and were finally heuristically (H) elucidated by talented scholars and researchers. Recently, new applications for the pumps open (O) to the surrounding fluid and diversity of the medium such as multiphase flow need more studies and some examples were briefly introduced to display the potential problems lastly.