Basic properties of the thermal decomposition reaction of ammonium dinitramide (ADN) were introduced. Theoretical investigation results of ADN decomposition reactions were summarized. The effect of solvent on the decomposition behavior of AND in the DN^- model was analyzed. The advantage of path for decomposition of different proton transfer isomers in dinitramide acid (HDN), HDN₂ and ADN₂ cluster model and the effects of the double proton transfer process of the intramolecular and intermolecular on the formation and decomposition reaction of different isomers were compared. The reason of trace water in (H₂O)_n…NH₄⁺[ON(O)NNO₂]^-(n=1, 2, 3)and ADN₂ cluster model on the abnormal decomposition behavior of ADN was discussed. Different theoretical model reveals the essence of the decomposition reaction of ADN to a certain extent, the kinetic parameters obtained in the larger ADN_n clusters agree with the experimental results well. Study shows that the introduction of the QM-MM method, which is suitable for the larger ADN_n clusters and solvation model in the liquid phase and gas phase, will play an important role to obtain the relevant thermodynamic and kinetic parameters of ADN involved in the application process.