This thesis is devoted to the theoretical study, by ab initio numerical methods, of the physical properties of substitutional semiconductor alloys. Nowadays, ab initio numerical methods allow to study quite accurately the physical properties of moderately complex periodic systems. These methods exploit the periodicity of the system, and can be applied to disordered systems (such as the substitutional semiconductor alloys), where the periodicity is lost, by replacing the original non-periodic system by a periodic one, which contains several unequivalent atoms in a large unit cell (supercell), distributed in such a way to reproduce the local atomic coordination present in the alloy. However, since this approximation is the better the larger the supercell used, an accurate description of disorder can require supercells so large (500 ÷ 1000 atoms) that the usual methods become too expensive and new techniques have to be developed. The chemical similarity between semiconductor components allows one to employ a perturbative approach in the study of their alloys. Exploiting the efficiency of modern perturbation techniques, we have been able to map the complex alloy problem onto much simpler models that, keeping the same accuracy of a complete first principles approach, can be easily studied with large supercells. By this approach, the structure, the thermodynamics, the lattice dynamics and the electronic structure of a few semiconductor alloys has been studied successfully.