Anelasticity of the earth was first discussed in terms of anelastic linear models. They are based on the linearized stress-strain relation of the attenuative medium. The stress-strain relation is characterized by a single relaxation time which is independent of frequency. Distortion of seismic waves viewed by an anelastic linear model can be characterized by the complex wave number of the model. The applicable frequency-range of the complex wave number is usually limited to a low frequency-range. However, the expressions of the attenuation factor and the corresponding phase velocity in the full frequency-range are necessary in order to obtain the impulse responses of the attenuative medium. The extrapolation of the applicable frequency-range to higher frequency gives the complex propagation function. The extrapolation must be done under the constraints that, (i) attenuation factor is nearly proportional to the first power of the frequency, (ii) the real and the imaginary parts of the complex propagation function must be related by a Hilbert transform pair, (iii) the complex propagation function must satisfy the crossing symmetry, and (iv) it must satisfy also the Paley-Wiener causality condition. At present, a truncated linear frequency attenuation model (Futterman), an almost linear frequency attenuation model (Kalinin et al.) and a power-law frequency attenuation model (Strick) have been proposed. The wave-forms of the impulse responses for these models are summarized, and some remarks on the mutual relations of these models are made. If a more precise frequency-dependence of the attenuation factor is obtained in a wide frequency-range from the frequency-range of the seismic surface wave to that of laboratory experiment, the distortion of the seismic source function through the attenuative medium can be estimated. Then, the calculated wave-forms of impulse responses can be compared with the observed ones. The validity of the frequency-dependence of the phase velocity of seismic body waves can be examined by the discrete Hilbert transform of the obtained attenuation factor.