Liquid crystals have been a major subject of research for the past decades. Aside from the variety of structures they can form, they exhibit a vast range of optical phenomena. Many of these phenomena found applications in technology and became an essential part of it. In this dissertation thesis we continue the line to propose a number of new applications of optical effects in liquid crystals and develop their theoretical framework. One such application is the possibility of beam combining using Orientational Stimulated Scattering in a nematic liquid crystal cell. Our numerical study of the OSS process shows that normally this possibility does not exist. However, we found that if a number of special conditions is satisfied efficient beam combining with OSS can be done. These conditions require a combination of special geometric arrangement of incident beams, their profiles, nematic material, and more. When these conditions are fulfilled, power of the beamlets can be coherently combined into a single beam, with high conversion efficiency while the shape and wave-front of the output beam are still of good quality. We also studied the dynamics of the OSS process itself and observed (in a numerical model) a number of notorious instabilities caused by effects of back-conversion iv process. Additionally, there was found a numerical solitary-wave solution associated with this back-conversion process. As a liquid crystal display application, we consider a nematic liquid crystal layer with the anisotropy axis modulated at a fixed rate in the transverse direction with respect to light propagation direction. If the layer locally constitutes a half-wave plate, then the thinscreen approximation predicts 100% -efficient diffraction of normal incident wave. If this diffracted light is blocked by an aperture only transmitting the zero-th order, the cell is in dark state. If now the periodic structure is washed out by applying voltage across the cell and light passes through the cell undiffracted, the light will pass through the aperture as well and the cell will be in its bright state. Such properties of this periodically aligned nematic layer suggest it as a candidate element in projection display cells. We studied the possibility to implement such layer through anchoring at both surfaces of the cell. It was found that each cell has a thickness threshold for which the periodic structure can exist. The anchored periodic structure cannot exist if thickness of the cell exceeds this threshold. For the case when the periodic structure exists, we found the structure distortion in comparison with the preferable ideal sinusoidal profile. To complete description of the electromechanical properties of the periodic cell, we studied its behavior at Freedericksz transition. Optical performance was successfully described with the coupled-mode theory. While influence of director distortion is shown to be negligibly small, the walk-off effects appear to be larger. In summary, there are good prospects for use of this periodically v aligned cell as a pixel in projection displays but experimental study and optimization need to be performed. In the next part we discuss another modulated liquid crystal structure in which the director periodically swings in the direction of light propagation. The main characteristic of such structure is the presence of bandgap. Cholesteric liquid crystals are known to possess bandgap for one of two circular polarizations of light. However, unlike the cholesterics the bandgap of the proposed structure is independent of polarization of normally incident light. This means that no preparation of light is needed in order for the structure to work in, for example, liquid crystal displays. The polarization universality comes at the cost of bandgap size, whose maximum possible value ∆ωPTN compared to that of cholesterics ∆ωCh is approximately twice smaller: ∆ωPTN ≈ 0.58∆ωCh if modulation profile is sinusoidal, and ∆ωPTN ≈ 0.64∆ωCh if it is rectangular. This structure has not yet been experimentally demonstrated, and we discuss possible ways to make it.