This work presents new development and applications of ab-initio simulation tools for material science. Focus lies on materials with strong electronic correlation and strong spin-orbit coupling. Improvements on methods for solving the impurity problem in LDA+DMFT is presented, as well as a reliant method for charge self-consistency in a LMTO based electronic structure code. A new adaptive scheme for Brillouin zone integration is developed, where we show a strong reduction of numerical noise compared to standard techniques. A reformulation of the standard LDA+U method aiming to reduce the number of free parameters is introduced. Fast and realistic reduction of the number of free parameters provides the possibility of high throughput calculations and enabled us to study a large number of compounds. An analysis method for polarization in terms of coupled multipoles, and their corresponding energy contributions is developed and applied. This led to the formulation of Katt's rules, a set of rules complementary to Hund's rules. Katt's rules applies for occupying the orbitals of an electronic shell with strong spin-orbit coupling. The analysis is also used to investigate the unconventional Uranium based superconductors URu2Si2, UPt3, UPd2Al3 and UNi2Al3, as well as the high temperature superconductor LaOFeAs. We also investigate the non-magnetic delta-phase of Plutonium, providing insight to the electronic structure and the branching ratios of 4d to 5f transitions seen in photo emission spectra.The influence of surface reconstruction on the magneto crystalline anisotropy is investigated in multilayer Fe/ZnSe, showing that Fe deposited on an unreconstructed interface strongly reduces the uniaxial component of the MAE. We provide a detailed understanding of the magnetic properties of Fe2P, opening possible routes for enhancing the MAE in this system. A general route to strong MAE in nano-laminates is presented, we apply this to propose a candidate with extremely strong anisotropy energy density, 5Fe/2W1-xReX for x=[0.6-0.8].