CONSPECTUS: Organic/inorganic hybrid structures are most exciting since one can expect new properties that are absent in either of their building blocks. They open new perspectives toward the design and tailoring of materials with desired features and functions. Prerequisite for real progress is, however, the in-depth understanding of what happens on the atomic and electronic scale. In this respect, hybrid materials pose a challenge for electronic-structure theory. Methods that proved useful for describing one side may not be applicable for the other one, and they are likely to fail for the interfaces. In this Account, we address the question to what extent we can quantitatively describe hybrid materials and where we even miss a qualitative description. We note that we are dealing with extended systems and thus adopt a solid-state approach. Therefore, density-functional theory (DFT) and many-body perturbation theory (MBPT), the GW approach for charged and the Bethe-Salpeter equation for neutral excitations, are our methods of choice. We give a brief summary of the used methodology, focusing on those aspects where problems can be expected when materials of different character meet at an interface. These issues are then taken up when discussing hybrid materials. We argue when and why, for example, standard DFT may fall short when it comes to the electronic structure of organic/metal interfaces or where the framework of MBPT can or must take over. Selected examples of organic/inorganic interfaces, structural properties, electronic bands, optical excitation spectra, and charge-transport properties as obtained from DFT and MBPT highlight which properties can be reliably computed for such materials. The crucial role of van der Waals forces is shown for sexiphenyl films, where the subtle interplay between intermolecular and molecule-substrate interactions is decisive for growth and morphologies. With a PTCDA monolayer on metal surfaces we discuss the performance of DFT in terms of interfacial electronic structure. We face the problem of a so far hidden variable, namely, electron-vibrational coupling, regarding level alignment at interfaces between organic and inorganic semiconductors. Poly(para-phenylene) adsorbed on graphene and encapsulated in carbon nanotubes represent case studies to demonstrate the impact of polarization effects and exciton delocalization in optoelectronic excitations, respectively. Polaron-induced band narrowing and its consequences for charge transport in organic crystals is exemplified for the HOMO bandwidth in naphthalene crystals. On the basis of these prototypical systems, we discuss what is missing to reach predictive power on a quantitative level for organic/inorganic hybrid materials and, thus, open a perspective toward the computational discovery of new materials for optoelectronic applications.