The lattice dynamics of perovskite oxides are investigated theoretically within the polarizability model which is a nonlinear approach taking into account anharmonic electron-lattice interactions. The emphasis is on local lattice anomalies which appear in the phonon modes dispersion. Above the actual phase transition temperature finite size polarized clusters appear at an onset temperature TBH which marks the precursor formation temperature. These local anomalies appear as well experimentally and are reviewed for various perovskite compounds.