The calculation of material properties usually requires a detailed understanding
of the interactions between the microscopic constituents. In my talk I will first
discuss a microscopically informed continuum theory which allows for accurate and efficient modeling of interacting inhomogeneous molecular liquids, such as liquid water, and the description of solvation processes and liquid-solid interfaces. Then I will discuss accurate theories to describe angle-resolved photoemission experiments. In particular, I will discuss two systems where many-electron interaction effects result in qualitative differences from the non-interacting (or mean-field) picture: in open-shell defects, electron-electron interactions cause a multiplet structure in the photoemission spectra. In doped graphene, the interaction of plasmons with the chiral Dirac fermions results in a reconstruction of the Dirac cone band structure. I will explain these observations using first-principles theories that include interactions beyond density-functional theory, such as ab initio GW theory and GW+cumulant theory.