Liquid crystal (LC) devices can be operated as amplitude modulators and phase modulators. LC amplitude modulation is commonly used in liquid crystal display (LCD) while phase-only modulation is useful for laser beam steering, tunable grating, prism, lens, and other photonic devices. Most LC devices are polarization dependent and require at least one polarizer. As a result, the optical efficiency is low. To enhance display brightness, a power hungry backlight has to be used leading to a high power consumption and short battery life. In a LC phase modulator, the polarization dependent property complicates the laser beam steering system. It is highly desirable to develop new operating mechanisms that are independent of the incident light polarization. In this dissertation, we have developed eight polarization-independent liquid crystal operation principles: three of them are aimed for displays and the other five are for phase modulators. For amplitude modulations, a new polymer-dispersed liquid crystal (PDLC) and two new dye-doped LC gels are polarizer-free by combining light scattering with dye-absorption effects. In phase modulation, we explore five device concepts: PDLC and Polymer-Stabilized Cholesteric Texture (PSCT), homeotropic LC gels, thin polymer film separated double-layered structure, and double-layered LC gels. In the low voltage regime, both PDLC and PSCT have a strong light scattering. However, as the voltage exceeds a certain level, the phase modulation is scattering-free and is independent of polarization. The homeotropic LC gels do not require any biased voltage and the response time is still fast. Although the remaining phase in these devices is small, they are still useful for micro-photonic device applications. To increase the phase change, thin polymer film separated double-layered structure is a solution. The orthogonal arrangement of top and bottom LC directors results in polarization independence. However, the response time is slow. Similarly, double-layered LC gels are not only polarization independent but also fast response due to the established polymer network.