Strong electronic correlation lies at the heart of modern condensed matter and material physics. An adequate treatment of the electronic correlation beyond standard band theory is a key to understand many unusual physical properties of strongly correlated materials such as Mott insulators and unconventional superconductors. In this talk, I will show how electronic correlation leads to dramatic modifications of the band theory predictions for the electronic structures in general, and the electron-phonon coupling and spin dynamics in particular in high temperature superconductors. I will demonstrate that first-principles electronic structure methods GW and dynamical mean field theory (combined with density functional theory) can account for the non-local and local electronic correlations, respectively, beyond standard band theory, and are useful tools to understand the microscopic mechanisms of high temperature superconductivity in (Ba,K)BiO3 and iron-based superconductors. For the former, electronic correlation leads to a strong enhancement of the electron-phonon coupling while for the latter, electronic correlation significantly strengthens the low-energy spin excitation, both of which favor higher superconducting temperature. In the end, I will discuss how we may use these first-principles methods to accelerate the discoveries of new functional materials with desired properties.
 Z. P. Yin, A. Kutepov, and G. Kotliar, Phys. Rev. X 3, 021011 (2013).
 Z. P. Yin, K. Haule, and G. Kotliar, Nat. Mater. 10, 932-935 (2011).
 Z. P. Yin, K. Haule, and G. Kotliar, Nat. Phys. 7, 294-297 (2011).
 Z. P. Yin, K. Haule, and G. Kotliar, Phys. Rev. B 86, 195141 (2012).
 Z. P. Yin, K. Haule, and G. Kotliar, to be published (2013).
 Z. P. Yin and G. Kotliar, EPL 101, 27002 (2013).
 M. Retuerto et al. Chemistry of Materials, 10.1021/cm402423x (2013).