In this thesis, various methods for studying solids by simulations of quantummechanical equations, have been applied to transition metals and their alloys. Transition metals such as Fe, Ni, and Mn, are not only cornerstones in modern technology, but also key components in the very fabric of the Earth interior. Such systems show highly complex magnetic properties. As shown within this thesis, to understand and predict their properties from a microscopic level, is still a highly demanding task for the the quantum theory of solids. This is especially crucial at elevated temperature and pressure.

It is found that the magnetic degrees of freedom are inseparable from the structural, elastic and chemical properties of such alloy systems. This requires theoretical descriptions capable of handling this interplay. Such schemes are discussed and demonstrated.

Furthermore, the importance of the description of Coulomb correlation effects is demonstrated by DFT calculations and also by going beyond the one-electron description by the LDA+DMFT method.

It is also shown how magnetic interactions in the half-metallic compound NiMnSb can be manipulated by alloying. The stability of these alloys is  also evaluated in calculations, and verified by experimental synthesis at ambient conditions.