Published by the American Geophysical Union as part of the Geodynamics Series, Volume 4. The fact that the materials in the solid parts of the Earth depart from perfectly elastic behaviour is now central to fundamental geophysical studies. Slow deformation (creep) by the processes of mantle convection has been widely recognised for about 25 years; it has been realised for much longer that seismic waves are attenuated but more recently there has developed a general if vague awareness of a probable correlation between high attenuation and low resistance to creep and in the last few years seismic attenuation has received much greater attention because it implies a first order dispersion of body waves (frequency dependence of elasticity).