We describe x-ray scattering studies of the nematic and smectic-A phases of the thermotropic liquid crystal 8CB and the Lα, and L3 (lamellar and sponge) phases of the lyotropic liquid crystal system: SDS, dodecane, pentanol and water. In the thermotropic system a series of orientational states of the nematic director is observed before entering the smectic-A phase where the smectic density wave and nematic director are oriented normal to the shear plane at high shear rates. In the lyotropic system lamellar fluctuations in the sponge phase (L3) become oriented by shear and in the lamellar phase (Lα) at high shear the layers orient preferentially along the velocity-gradient direction, in highly anisotropic cylindrical multilamellar liposome-like structures.