The title reaction has a great deal of intriguing characters and provides energy for a chemical laser, and of much theoretical and experimental interest. Accurate description of the F 1 H 2 ! HF 1 H and F 1 HD ! HF/DF 1 D/H reaction within the Born-Oppenheimer approximation presents a great challenge to the capabilities of modern quantum chemistry methods. The FHH system, which has strongly coupled eleven electrons, requires elaborate quantum chemistry calculations in the determination of potential energies with high accuracy. Moreover, a quantum reaction dynamics calculation for the F 1 H 2 / HD reaction requires much computational effort due to its large exothermicity. After more than half a century's endeavor, now we are capable of describing the F 1 H 2 /HD reaction close to spectroscopic accuracy. In this article, a brief review of the development of the potential energy surfaces and quantum reaction dynamics of the title reaction and its isotope substitutes is presented. Some of the results by quantum reactive scattering theory using the latest several typical potential energy surfaces are given, along with the corresponding experimental measurements, to illustrate the current stage of our capability on describing the F 1 H 2 /HD reaction.