The basis of density functional theory and its extension to magnetic systems is reviewed in the first chapter. The second chapter describes the implementation of the fully relativistic ultrasoft pseudopotential method whose predictive power is tested by calculating the spin-orbit splitting in the band structure of two bulk systems: Au-fcc and Pt-fcc. In the third chapter the magnetic properties of several Co based nanostructures are described as a function of their dimensionality, going from 2D to 0D systems. Finally, in the fourth chapter, the physical properties of a novel class of molecular nanomagnets are discussed. Mathematical developments and details of some of the topics mentioned during the thesis are reported separately as appendices.