Atomic-and continuum-scale computer simulation techniques have now become sufficiently powerful that many phenomena associated with radiation damage effects in metals can be modelled with a high degree of realism. Recent studies of several such phenomena are reviewed here. Primary knock-on atoms (PKAs) that recoil under collision from energetic atomic particles such as neutrons or ions are the principal source of damage. At high enough recoil energy, they create cascades of atomic displacements that result in single and clustered self-interstitial and vacancy defects. The time and length scales of the cascade process are ideally suited to atomic-scale computer simulation by molecular dynamics (MD). This method provides data on the number of defects produced and their distribution in clusters. This information was not available from earlier models and so the nature of the primary damage state is now much clearer. MD is also being used to reveal the nature of the motion and interaction of defects. Prediction and understanding of mechanical properties of irradiated metals requires simulation of dislocation-obstacle interactions. Models based on the continuum approximation are now being extended by large-scale MD simulations of the motion of dislocations gliding through irradiation-induced features such as voids and precipitates, and these reveal the strength and weakness of the earlier studies. Dynamic effects at temperatures greater than 0 K are also being investigated. The place of modelling in the multiscale problems of radiation damage is emphasised.