Recognition of confirmation of impact structures  need to be supported by evidence of shock metamorphism (such as shatter cones, planar deformation features in quartz, etc.) and/or by traces of extraterrestrial matter (e.g., iridium anomalies, osmium isotopes). Impact cratering differs mainly from other surface geological processes by the extreme pressures, temperatures, and high strain rates involved, and by the almost instantaneous nature of the impact process. a multidisciplinary approach to research is required to improve knowledge of the cratering process. After a review on impact cratering, 2D and 3D numerical modeling of impact craters will be presented, some of them combined with geological and petrographical observations.