The (Q)HA breaks down in multiple cases. Most strikingly, this happens when imaginary phonon modes are present in the harmonic phonon dispersion. This is the case in displacive phase transitions in general and for several technologically important materials, including the aforementioned perovskite family. Even for a seemingly simple material such as NaCl, predictions of some thermal properties are inaccurately described within the QHA. . Anharmonic theories extend the reach of phonon-based approaches significantly beyond the (Q)HA.