Structural phase transitions of the tilting variety occur and transform certain cubic antifluorite and cubic perovskite structures to lower symmetry structures. This article provides a review of recent advances in our understanding of these phase transitions as revealed by pure nuclear quadrupole resonance (NQR) experiments in K 2PtBr 6, K 2ReCl 6, CsPbCl 3, and K 2OsCl 6. In general, the results show that both NQR frequency and spin-lattice relaxation data may be analyzed to reveal the condensation of the rotary-lattice mode responsible for a particular transition. The similarity of the antifluorite and perovskite structures with respect to tilting type phase transitions is illustrated both by the behavior of the NQR data and by the results of rigid-ion model calculations. In particular, the K 2PtBr 6 data provide experimental confirmation of the dominance of the anharmonic Raman process as a relaxation mechanism for the bromine nuclei. The K 2ReCl 6 data provide an example for analysis in which the temperature dependence of the NQR frequency data is dominated by specific volume effects. The CsPbCl 3 relaxation data reflect the extraordinary degree of anharmonicity present in the cubic phase. The substance K 2OsCl 6 provides evidence for the formation of tetragonal phase dynamic clusters in the cubic phase. In all instances the interpretation makes use of available information from other types of experiments. For example, the NQR frequency spectrum of CsPbCl 3 is shown to be consistent with structural determinations from neutron scattering studies.