The radiation damage is one of the key concerns in the research of materials used in radiation environments. In this thesis, we theoretically investigate the radiation damage phenomenon by focusing on two important topics: the defect production and evolution, and the defect characterization. 

The first part aims at two aspects. Firstly, a full energy range primary radiation damage model is presented based on modifying the athermal recombination corrected displacements per atom (arc-dpa) model. This modified full energy range model is validated by classical and ab initio molecular dynamics. Then, the modified model is used to estimate the radiation damage in electron-irradiated iron alloys and perform a systematic cluster dynamics study. The Cu precipitation in experiment is reproduced by the cluster dynamics model. This model is then used to predict the Cu precipitation in spent-fuel canisters up to 10⁵ years. 

The second part focuses on positron annihilation in metallic materials. Positron annihilation spectroscopy (PAS) is a useful technique to characterize the ultrafine defects in materials. In this part, the state-of-the-art two-component density functional theory (TCDFT) is used to calculate the positron annihilation characteristics (positron lifetimes and Doppler broadening spectra) in materials. Firstly, a case study is performed in Fe-Cu system. Both vacancyfree Cu clusters and vacancy-Cu complexes are investigated. Then, a more systematic investigation is conducted to calculate the positron annihilation in transition metals. Finally, the positron annihilation in vacancy defects in tungsten is investigated by combining both experimental and theoretical results. The limitation of commonly used Boroński-Nieminen local density approximation is discussed.