This work is devoted to a comprehensive detailed study of a pure zirconium with non-equilibrium point defects induced by irradiation within the framework of the multiscale modelling scheme by using quantum-mechanics methods, molecular dynamics, and the Monte-Carlo methods based on the Langevin dynamics. By using $ab$-$initio$ calculations, the structural, electronic, and energy properties of a pure zirconium with isolated vacancies and their clusters are studied. The lattice-parameter change in pure zirconium with different concentrations of isolated vacancy and different configurations of di- and trivacancies is discussed. The vacancy-formation energy in a pure zirconium is obtained. Stability of small vacancy clusters containing divacancy characterized by different distances between two vacancies as well as trivacancies of different configuration is analysed. Distributions of electron density, band structure, and Fermi surface for pure zirconium with isolated vacancy are studied in detail. We calculate the dependence of the Fermi energy of a zirconium crystal, whose unit cell contains a vacancy cluster, on the number of vacancies in the cluster. Cascade formation, development, and annealing in pure zirconium crystals irradiated in different irradiation conditions are studied within the framework of the molecular-dynamics simulations. Statistical and geometric properties of cascades are examined in detail by varying sample temperature, energy of primary knocked atom, and direction of its motion. A possibility of channelling at cascades’ development resulting in formation of crowdions is shown. A change in statistical properties of the crystal during cascade development and relaxation time of cascades is calculated. Dependence of formation energy of point defects and vacancy clusters on temperature is discussed. Spatial self-organization of an ensemble of point defects in $\alpha$-zirconium irradiated by fast neutrons by using reaction rate theory is studied. In our consideration, we take into account elastic properties of the medium due to defects’ presence and sink density dynamics. We consider dynamics of the system with uniform distribution of point defects and spatially extended system at different irradiation regimes (by varying irradiation temperature and dose rate). As found, the point defects’ patterning is accompanied by a formation of vacancy clusters. The distribution of elastic fields with the self-organization of a vacancy ensemble in a pure zirconium subjected to shear and cyclic deformation and the impact of irradiation on the mode of deformation of zirconium are studied.