Impact craters observed on the planetary surfaces have been formed by celestial body impacts. Such impacts can also disrupt celestial bodies if their energy is sufficiently large. In this short paper, mathematical and physical models of celestial body impacts are reviewed, focusing on the impact cratering process which is commonly divided into three stages: the contact and compression stage, the excavation stage, and the modification stage. The contact and compression stage determines the initial thermodynamic state immediately after impact. During the excavation stage, transient cavity formation and target material ejection are caused by excavation flow. The transient cavity is modified by gravity in the modification stage, and then a final crater is formed. Shock wave and gravity play an important role during these stages because celestial body impacts are characterized by their high speed(>〜km/s) and large scale. Scaling laws derived from dimensional analysis are also described.
