This paper reviews some of the recent advances in the modeling of anomalous thermodynamic properties. Inelastic neutron scattering experiments in combination with lattice dynamics calculations are used to study the phonon properties as well as thermodynamic properties of several novel compounds. There is a large variation in the thermal expansion, specific heat and equation of state pertaining to the compounds described in this review. The interatomic potentials as determined for various compounds have been able to successfully model the thermodynamic behavior. Lattice dynamical calculations and high pressure inelastic neutron scattering experiments indicate that large softening of several low energy phonons is mainly responsible for the negative thermal expansion in ZrW2O8, HfW2O8 and ZrMo2O8 UP to 1443, 1050 and 600 K, respectively. It has been shown that a proper description of negative thermal expansion requires consideration of both the acoustic and optic phonon modes in the entire Brillouin zone. We have also reviewed studies on X-ray image storage materials MFX (M = Ba, Pb, Sr; X = Cl, Br, I); compounds MPO4 (M = Al, Fe and Ga); several garnet minerals M3Al2S13O12 (M = Fe, Mg, Ca and Mn) and zircon (ZrSiO4). The variations in phonon spectra manifest in the thermodynamic properties of these compounds at high pressure and temperature. The calculations enable predictions and microscopic interpretation of the thermal expansion, specific heat and the equation of state. (c) 2005 Elsevier Ltd. All rights reserved.