The seismology is the most effective method to explore the Structure of subduction zones to great depth. The distinguishing feature of the mantle in the subduction regions is the presence of hydrated phases, which transport water into the Earth's interior and release it with dramatic local consequences, triggering earthquakes and melting. The seismological detection of these hydrous phases and geo-dynamic interpretation of flow in the hydrous mantle depend on knowledge of the anisotropic elastic properties and the characteristics of the wave propagation in anisotropic media. In this paper we briefly recall the distinguishing features of anisotropic wave propagation and the observable parameters. We suggest the Vp/Vs ratio is a physically sound parameter than can be observed by seismology in anisotropic regions of the Earth, whereas the Poisson's ratio, which is often quoted, is not directly observable and does not correspond to the characteristics of wave propagation in an anisotropic or isotropic medium. We report for the first time the ratios of Vp/Vs1 and Vp/Vs2, where Vs1 is the fastest and Vs2 slowest S-wave velocities of an anisotropic media. We present the current knowledge of the anisotropic seismic properties of hydrous minerals in the upper mantle, transition zone, and lower mantle that are stable along low temperature geotherms associated with subduction, and identify which minerals are likely to influence seismological observations because they have very high volume fractions, or very high anisotropies, or both of these.;In the upper mantle antigorite and talc are exceptionally anisotropic (Vp 71% Vs 68% and Vp 65%, Vs 68%, respectively) and chlorite is also very anisotropic for S-waves (Vp 35%, Vs 76%). Comparatively less anisotropic are hornblende (Vp 27%, Vs 31%), used as proxy for tremolite in subduction zones, and clinohumite (21.8%, Vs 15.9%). Brucite at 4 GPa (Vp 26.5%, Vs 30.9%) and the dense hydrogen magnesium silicate (DHMS) phase A at 9GPa (Vp 9.3%, Vs 17.6%) are the only hydrous minerals stable in the upper mantle that have had their elastic properties measured at in situ mantle pressures. Except for the phase A, all these minerals are more anisotropic than olivine for at least one parameter (Vp, Vs, Vp/Vs1, or Vp/Vs2). In the transition zone the major phases hydrous wadsleyite and ringwoodite C have moderate to weak anisotropies (Vp 16.3%, Vs 16.5%, and Vp 1.9%, Vs 4.4%, respectively). The DHMS Superhydrous B has a moderate anisotropy (Vp 6.9%, Vs 11.6%). At greater depth the DHMS phase D Lit 24 GPa (Vp 10.8%, Vs 18.0%) is the only hydrous phase that can transport hydrogen from the transition zone into the lower mantle. The phase D is more anisotropic for S than P waves like many of the hydrous phases. From these data it is clear that hydrous phases are in general very anisotropic. However, pressure can play a strong role in reducing anisotropy. It is the case for brucite and talc, in which increasing pressure from ambient to 4 GPa reduces the anisotropy by about 50% for both P and S waves. In contrast, the anisotropy of the DHMS phase A does not change significantly with pressure.;Our picture of the seismic anisotropy of hydrated minerals remains incomplete; the elastic properties of many have not been measured even at ambient conditions (e.g., 10 angstrom phase and phase E) or not measured in their true elastic symmetry (e.g., clinochlore). The majority of hydrous minerals have not been measured at high pressure. and none related to hydrated mantle have been measured at elevated temperature. We have shown in the few cases where hydrous minerals have been measured as a function of pressure, that this variable has an important effect oil the velocity distribution and in most cases reduces the degree of anisotropy, hence we Would expect seismic anisotropy to play a key role in the determination of the shallow structure of subduction zones in the upper mantle.