Octogen(HMX) is one of the most widely used energetic materials. Research progress in the two molecular conformation structures, electronic structure properties and molecular thermal stability of HMX and the stacking structure and thermal stability of HMX-based crystals were reviewed. The essential difference between the conformational stability of HMX and the thermal stability of HMX-based crystals were analyzed from the molecular angle and crystal packing structure. The kinetic and thermodynamic data of different decomposition mechanisms were compared. It is considered that the future research should focus on exploring the transformation mechanism and thermodynamic properties of each crystal form of HMX, preparing new HMX cocrystals and understanding the formation mechanism,and establishing more accurate simulation calculation method for HMX.