The paper introduces a new type of anisotropic liquid crystal - core optical fibers and in particular focuses on two aspects. First, studying theoretically the preferred direction of the nematic liquid crystal director field inside a hollow core optical fiber we have derived characteristic formulas for the basic modes TE01 and TM01 by using the Maxwell equations and Frank free energy to find the director distribution. Second, we have investigated experimentally influence of selected environmental parameters such as temperature, AC external electric field and hydrostatic pressure on the light transmission through liquid crystal fibers. These studies have demonstrated the feasibility of using optical hollow core fibers filled with liquid crystal to build switches, modulators and all-fiber sensors.