Real Earth media are anelastic, which affects both the kinematics and dynamics of propagating waves: Waves are attenuated and dispersed. If anelastic effects are neglected, inversion and migration can yield erroneous results. The anelastic effects in real rocks can be well described by a viscoelastic model. Hence, viscoelastic wave propagation simulation is a well suited base for realistic seismic inversion algorithms derived through the adjoint state technique. The thesis develops a finite-difference simulator to model wave propagation in viscoelastic media. The viscoelastic scheme, which is dispersion and stability analyzed, is only slightly more expensive than analogous elastic schemes. The thesis also presents a method for modeling of constant Q as a function of frequency based on an explicit closed formula for calculation of the parameter fields. The τ-p (intercept time-slowness) domain permits economical modeling and inversion of 3-D wave propagation in attenuative (viscoacoustic) layered media. A recomputation scheme for adjoint calculations permits efficient inversion in multidimensional attenuative (viscoacoustic) physically consistent media. The inversion method is proved to be feasible by successfully being applied to real field data. Synthetic data inversion shows that neglect of attenuation can lead to interpretation errors. Analysis in thesis indicate the necessary precision in attenuation (Q) to reliably estimate Earth parameters, such as velocity and density. Attenuation has a large effect on the magnitude of inversion estimates of Earth parameters, however ratios (relative amplitudes) between parameters are not as sensitive to the amount of attenuation in the medium. This is a positive result since the amount of attenuation in a medium is rather difficult to determine accurately from (seismic) data. Hence, a reasonably well estimated amount of attenuation would allow for reliable estimation of Earth parameter ratios, such as the ratio between normalized velocity and density fluctuations. Ratios between estimated Earth parameters are generally having an extreme point for the correct amount of attenuation. If this extremum does not exist, the ratios are well determined. The existence of an extreme point could be the base for estimation algorithms for attenuation, through search for the extreme point in Earth parameter ratios as a function of attenuation.