Anisotropic fluids are widespread, ranging from liquid crystals used in displays to ordered states of a biological cell interior. Optical trapping is potentially a powerful technique in the fundamental studies and applications of anisotropic fluids. We demonstrate that laser beams in these fluids can generate anisotropic optical trapping forces, even for particles larger than the trapping beam wavelength. Immersed colloidal particles modify the fluid's ordered molecular structures and locally distort its optic axis. This distortion produces a refractive index ''corona'' around the particles that depends on their surface characteristics. The laser beam can trap such particles not only at their center but also at the high-index corona. Trapping forces in the beam's lateral plane mimic the corona and are polarizationcontrolled. This control allows the optical forces to be reversed and cause the particle to follow a prescribed trajectory. Anisotropic particle dynamics in the trap varies with laser power because of the anisotropy of both viscous drag and trapping forces. Using thermotropic liquid crystals and biological materials, we show that these phenomena are quite general for all anisotropic fluids and impinge broadly on their quantitative studies using laser tweezers. Potential applications include modeling thermodynamic systems with anisotropic polarization-controlled potential wells, producing optically tunable photonic crystals, and fabricating light-controlled nano-and micropumps.colloids ͉ laser tweezers ͉ liquid crystals ͉ optical trapping ͉ defects