Recent progress in first-principles methods for computing the electronic structure of correlated materials

Substantial progress has been achieved in the last couple of decades in computing the electronic structure of correlated materials from first principles. This progress has been driven by parallel development in theory and numerical algorithms. Theoretical development in combining ab initio approaches and many-body methods is particularly promising. A crucial role is also played by a systematic method for deriving a low-energy model, which bridges the gap between real and model systems. In this article, an overview is given tracing the development from the LDA+U to the latest progress in combining the GW method and (extended) dynamical mean-field theory (GW+EDMFT). The emphasis is on conceptual and theoretical aspects rather than technical ones.