Abstract: The present paper givea review on the development and current achievements in explosionmechanics and impact dynamics, including constitutive relation ofmaterial, damage evolution, and fracture, shock-induce phasetransition, jet and material ejection etc., among which thedevelopment of constitutive relation of material is relativelysystematic. There are several typical models that may be of valuefor reference, i.e. they can not only be widely applied, but alsobe used to check up and make contrast with experimental data. Asfor damage, only phenomenological models with different physicsmechanisms involved have been proposed up to now, and they are inurgent need of direct verification of experiment data. Thetechnique of jets is widely applied to engineering practice,however, there are scarcely profound theoretical studies.Investigation on material ejection also remains in a qualitativestage. With the development of experimental techniques andinstrumentation for measurement, some encouraging developmentshave been achieved in interrelated fields due to untiring work ofscientists and engineers.