This licentiate thesis is made up of two parts, the first part is concerned with quantum spin liquids and the second part is about RIXS interferometry on cluster Mott insulators. Quantum spin liquids are fascinating phases of matter, which lack long-range magnetic order at zero temperature due to magnetic frustration. They are known to exhibit long-range entanglement and have fractionalized excitations. In this thesis we study spin-orbital liquids. They belong to a family of generalized Kitaev spin liquids, which are exactly solvable models of quantum spin liquids. We generalize the spin-orbital model to a three- and a four-coordinated three-dimensional lattice and study the impact of symmetries and exactly solvable perturbations on the low-energy physics. The second part of the thesis is concerned with cluster Mott insulators, and how they can be probed using resonant inelastic X-ray scattering (RIXS). Cluster Mott insulators are materials in which strong electron-electron interactions force the electrons to localize on clusters of atoms. They thus form “molecules” within the solid, which give rise to interference patterns in the RIXS intensity. These interference patterns do not only inform us about the existence of quasimolecular states, but also about their character. We discuss RIXS interferometry on the trimer iridate Ba4NbIr3O12.