Experimental data in some amorphous, glassy and quasicrystalline mater
ials suggest heat transport due to phonon hopping. A necessary prerequ
isite of such transport mechanism is the localization of vibrational s
tates and anharmonicity induced interaction between these states. A th
eoretical study of phonon hopping requires the derivation and solution
of corresponding rate equations. The above problems will be criticall
y discussed, in particular the formal relationship between phonon and
electron hopping.