This paper describes a number of experimental methods that have been used to measure the internal energy loss that occurs in many solids, especially high polymers, when they are taken around deformation cycles. This loss can be measured directly, but when its magnitude is small and when the response is linear, it is found to be proportional to four other quantities: namely, the logarithmic decrement of free oscillations of systems where the material is used as a restoring elastic element, the sharpness of resonance of forced oscillations of such systems, the angle by which the strain lags behind the stress in sinusoidal oscillations, and the attenuation coefficient of sinusoidal waves propagated through the material. The magnitude of this mechanical loss is found to vary with the frequency of the oscillations, and these variations can be correlated to microscopic processes taking place in the solid. A variety of experimental techniques have to be used to cover the large ranges of frequency that are needed in order to study such correlations and it is highly desirable that all the measurements be for the same type of mechanical deformation (for example, shear). The results of measurements extending over about ten decades of frequency are reviewed, and the interpretation of these in terms of the various microscopic processes in the material are discussed.