In a carbon-free economy, nuclear power will surely play a fundamental role as a clean and cost-competitive energy source. However, new-generation nuclear concepts involve temperature and irradiation conditions for which no experimental facility exists, making it exceedingly difficult to predict structural materials performance and lifetime. Although the gap with real materials is still large, advances in computing power over the last decade have enabled the development of accurate and efficient numerical algorithms for materials simulations capable of probing the challenging conditions expected in future nuclear environments. One of the most important issues in metallic structural materials is the degradation of their mechanical properties under irradiation. Mechanical properties are intimately related to the glide resistance of dislocations, which can be increased severalfold due to irradiation-produced defects. Here, we present a combined multiscale study of dislocation-irradiation obstacle interactions in a model system (Cu) using atomistic and dislocation dynamics simulations. Scaling laws generalizing material behavior are extracted from our results, which are then compared with experimental measurements of irradiation hardening in Cu, showing good agreement.