This thesis describes the development and applications of the continuum-atomistic molecular dynamics (MD) model in the context of radiation damage. By extending the classical MD method to incorporate the electronic excitations represented as an electron fluid and coupled to the ions in the two-temperature (2T) formalism, we have been able to correctly capture the physics governing the atomistic dynamics under huge electronic excitations. The integrated 2T-MD model has been specifically adapted to study three types of non-equilibrium scenarios: laser excitations, swift heavy ion impacts and large-scale high energy collision cascades. Using the 2T-MD model we have estimated the impact of the electron-phonon coupling and the electronic stopping power on the primary radiation damage yield in bcc iron. We have found that the cascade dynamics and the resultant damage from 50-100 keV primary knock-on atom impacts is highly sensitive to the electronic stopping treatment at low projectile velocities, which represents the first rigorous study of this type. By examining the temporal evolution of the structure factor of laser-irradiated gold thin films, we have been able to directly compare the 2T-MD results with Bragg peaks measured by ultrafast electron diffraction and have achieved an excellent agreement between theory and experiment with no fitting parameters. This has enabled us to elucidate the melting dynamics following laser irradiation at a picosecond resolution for the first time and also to validate the two-temperature approach. To simulate semiconductors under electronic excitations, the continuum part of the 2T-MD model, which represents electrons, has been replaced by two continuum equations: one for carrier density and one for their energy, to account for the finite band-gap effects. We have applied such extended method to simulate ion tracks, which result from swift heavy ion impacts. We have achieved a very good agreement with the experimental results on the ion track radii, provided that we are free to adjust the strength of the electron-phonon coupling. We propose future studies in the field of non-equilibrium atomistic modelling. In particular, we discuss ab initio methods and further improvements to hybrid MD to study the effects of the interatomic potential changes in response to high electronic excitations
