In this contribution we introduce an electronic-structure-theory-based approach to a quantum-chemical thermochemistry of solids. We first deal with local and collective atomic displacements and explain how to calculate these. The fundamental importance of the phonons, their dispersion relations, their experimental determination as well as their calculation is elucidated, followed by the systematic construction of the thermodynamic potentials on this basis. Subsequently, we provide an introduction for practical computation as well as a critical analysis of the level of accuracy obtainable. We then show how different solid-state chemistry problems can be solved using this approach. Among these are the calculation of activation energies in perovskite-like oxides, but we also consider the use of theoretical vibrational frequencies for determining crystal structures. The pressure and temperature polymorphism of elemental tin which has often been classically described is also treated, and we energetically classify the metastable oxynitrides of tantalum. We also demonstrate, using the case of high-temperature superconductors, that such calculations may be used for an independent evaluation of thermochemical data of unsatisfactory accuracy. Finally, we show the present limits and the future challenges of the theory.