Contemporary galaxy redshift surveys map out the distribution of galaxies in the universe in great detail. The clustering of galaxies measured from such surveys has become a powerful probe of cosmology and galaxy formation and evolution. I will talk about the anisotropic patterns in galaxy clustering and discuss what we can learn about cosmology and galaxy formation from such anisotropies. I will first focus on a case of anisotropic clustering with a gravitational origin (known as redshift-space distortion), and highlight our recent work on the relative kinematics between galaxies and dark matter halos inferred from such an effect with SDSS/SDSS-III data. Then I will move to a case of anisotropic clustering with a non-gravitational origin, which may arise due to radiative transfer effect for a population of high-redshift star-forming galaxies (known as Lyman-alpha emitting galaxies). The profound implications in cosmology and galaxy formation and the current observational status will be discussed.