Electronic structure theory today covers virtually all aspects of condensed matter theory - from light-element molecules to heavy-element periodic solids, structural, electronic and vibrational ground state and excited states, etc. From a computational point of view, one would like to have all these properties accessible within the same, computationally efficient and accurate framework. We here describe the Fritz Haber Institute ab initio molecular simulations (FHI-aims) package [1] for all-electron simulations of molecules and solids, using numeric atom-centered orbitals as the quantum-mechanical basis set. The primary production method is density functional theory (LDA, GGA), with a strong development focus on approaches "beyond DFT" (Hartree-Fock, hybrid functionals, MP2, RPA, or GW for electronic spectroscopic properties). FHI-aims performs efficiently for systems up to thousands of atoms, and also on massively parallel platforms with possibly thousands of CPUs (e.g., BlueGene). The presentation touches on three sets of physical results: (i) the first-principles prediction of the secondary structure and dynamical properties of a class of "benchmark" polyalanine biomolecules, (ii) a direct density functional theory assessment of surface structure [the large-scale reconstructions of Au(100) and Pt(100)] surfaces, and (iii) paths "beyond DFT" for specific surface problems [e.g., CO/Cu(111)].