Some physical aspects of high velocity (> 30 km=s) collisions involving an asteroid or comet nucleus are discussed. Impacts by both meteoroids and massive artificial objects are considered; these may result in effects such as gas expansion reaction forces, shock wave propagation, and fragmentation. The approach is based on conservation laws and observed phenomena associated with high energy impacts, combining data on the attenuation of strong and weak shock waves in rocks and data on the strength of meteorites as determined by their observed breakups in the atmosphere. The calculations accept the prevailing view that asteroids are structurally inhomogeneous and contain some initial crack distribution, possibly of the type that has been observed in meteorites. Analytical estimates for the mean fragment size distribution and the volume of a fragmentation zone are derived from a step-by-step analysis of the wave evolution. This leads to the surprising conclusion that a powerful impact can cause the complete disruption into small pieces of a much larger monolithic asteroid (1-2 km in diameterFby an impact with a kinetic energy of less than 1 MtΓ than previously thought. In particular, an artificial very massive projectile might be assembled from low-orbit space debris (dead satellites, abandoned space stations, etc.). This suggests that kinetic energy impacts are a viable alternative to nuclear explosions, which other authors have concluded as that required to protect the Earth from an asteroid on a collision course. Recent experimental and theoretical results are also used to compare the total change of asteroid momentum due to a high energy impact to the momentum produced by gas expansion, and also to that resulting from a nuclear explosion.