Abstract: A thorough understanding of electronic structure and optical properties is essential to the discovery of new phenomena in many classes of materials. Quantities of interest could include the band structure, optical absorption, excitonic features, and much more. First principles calculations allow us to make such predictions even when established models fail and therefore help us develop new intuition. Preferably, we would like to use density functional theory (DFT) for such calculations, because the relative computational simplicity afforded by DFT allows us to attack realistic problems. Unfortunately, despite many other successes, DFT has traditionally struggled with prediction of the above quantities. Specifically, research has been fraught with very difficult questions as to the extent to which spectroscopic conclusions can be drawn from DFT even in principle, followed by serious concerns as to the reliability of typical DFT approximations in practice. In this lecture, I will focus on new formal and practical approaches which offer fresh answers to the above long-standing questions. In particular, I will introduce optimal tuning of range-separated hybrid functionals as a means to mimic successfully, in many cases, the quasi-particle picture of many-body perturbation theory, thereby allowing for quantitative calculations of both single- and two-particle excitations. I will show how this is achieved for finite systems, present some generalizations to solids, and discuss limitations and remaining challenges.