Abstract: We investigate the question as to whether disordered harmonic crystals in two and three dimensions have a finite thermal conductivity. A heuristic argument using localization theory and kinetic theory is given to estimate the system size dependence of the current. Numerical results testing these predictions will be discussed. The numerical studies are based on the Landauer formula using phonon transmission and also on nonequilibrium simulations. The role of ballistic and diffusive phonon modes and the effect of boundary conditions are critically analyzed. The effect of anharmonicity will also be briefly discussed.