For decades, ab initio calculations have been largely viewed as being restricted to 0K, or more precisely, as being condemned to operate without the concept of temperature at all. Nowadays, this major constraint has been lifted, and routine methods to evaluate vibrational properties and temperature dependent thermodynamic functions have become available, at least within the harmonic approximation. In this contribution, the basic concepts of the so-called direct approach [1,2] to vibrational properties are summarized and a number of applications in rather diverse fields are discussed. In a routinely manner, free energies, vibrational enthalpies and entropies of solid compounds can be evaluated, thus enabling the study of thermochemistry of chemical reactions as well as phase stability from ab initio theory. As will be shown, in particular for hydrogen containing compounds, neglecting zero point vibrations may cause qualitatively wrong answers in many cases. In addition, phonon instabilities of metastable phases may point towards possible phase transformations to other stable phases. Furthermore, vibrational spectra of transition states are well suited for the study of chemical kinetics as well as transport properties, opening the field for simulating diffusion processes. The methodology is, however, not restricted to the solid state: vibrations of molecules and molecules on surfaces may help to analyze spectral data, and the calculation of surface phonons are well suited to confirm stability of a suggested surfaces or may reveal possible reconstructions, just to mention some of the rather promising though challenging applications. Complementing the successful case studies, possible computational issues and difficulties are discussed thus providing a critical assessment of the methodology.

[1] K. Parlinski, Z. Q. Li, Y. Kawazoe, Phys. Rev. Lett. 78, 4063 (1997)
[2] G. Kresse, J. Furthmüller, J. Hafner, Europhys. Lett. 32, 729 (1995)

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