Abstract: Nuclear thermal propulsion (NTP) is a new conceptual propulsion technique of high specific impulse and large thrust, in which the hydrogen coolant is heated to a high pressure and high temperature condition by fission energy originating from the nuclear reactor, and then ejected from a convergent-divergent nozzle at high speed to generate thrust. At present, NTP is regarded as one of the most promising technologies which can be applied to manned deep space exploration in the near future. There exist solid core, liquid core and gas core in history, among which the solid core is the most mature. Totally, the reactor is compact with high power-density and high temperature, which requires matching thermal hydraulics design to ensure the heat transfer safety. In this paper, the typical thermal hydraulics processes were summarized based on the investigation of NERVA, PBR, MITEE, and CERMET of United States and RD-0410 of Soviet Union. In addition, the associated key technology challenges were presented and analyzed. The analysis result will provide some references for the study and design of space nuclear thermal propulsion system of our country.