We compile the experimental data on deformation of hydrated olivine single crystal to determine the influence of water and pressure. We analyse the data from low pressure (P = 0.1 MPa and 0.1-0.3 GPa) high-resolution experiments as well as the results from higher pressures (2 to 6 GPa) containing larger uncertainties, using a flow law of the form (epsilon) over dot(i) = (epsilon) over dot(i)(dry) + (epsilon) over dot(i)(wet) with (i:slip system). The data are normalized to a common stress (150 MPa) and temperature (1573 K) and we determine the parameters water content exponent (r) and activation volume (V*). We found largely different values of r and V-* for different orientations (slip systems) implying that the influence of water and pressure is highly anisotropic providing largely different values of r and V-*. For the (c) orientation where the (010) slip system is activated, we obtain r() = 0.35 +/- 0.08, and V* () = 11.0 +/- 3.0 cm(3)/mol, while for the (c) orientation where the (010) slip system is activated, r() = 1.3 +/- 0.30, and V*() = 5.6 +/- 3.6 cm(3)/mol (for a fixed water content). The highly anisotropic effects of water and pressure suggest that creep in olivine is not controlled solely by diffusion but also controlled by the density of jogs (or kinks) on dislocations that is controlled by water and pressure. We find that the easier slip system changes from the a-slip (slip along the  direction) at low water content and low pressure to the c-slip (slip along the  direction) at high water content and high pressure, suggesting that the c-slip is softer than the a-slip in most of the asthenosphere, whereas the opposite is true in most of the lithosphere. Implications of these results are discussed using a model of deformation of a polycrystalline aggregate made of anisotropic crystals. It is suggested that in the asthenosphere where most of plastic deformation occurs, short-term time dependent small strain deformation associated with post-seismic and post-glacial deformation is dominated by the c-slip and strongly dependent on the water content, whereas the long-term large strain deformation associated with mantle convection is dominated by the a-slip that is only weakly dependent on water content.