Liquid crystals (LCs) are important materials for flat panel display and photonic devices. Most LC devices use electrical field-, magnetic field-, or temperature-induced refractive index change to modulate the incident light. Molecular constituents, wavelength, and temperature are the three primary factors determining the liquid crystal refractive indices: ne and no for the extraordinary and ordinary rays, respectively. In this dissertation, we derive several physical models for describing the wavelength and temperature effects on liquid crystal refractive indices, average refractive index, and birefringence. Based on these models, we develop some high temperature gradient refractive index LC mixtures for photonic applications, such as thermal tunable liquid crystal photonic crystal fibers and thermal solitons. Liquid crystal refractive indices decrease as the wavelength increase. Both ne and no saturate in the infrared region. Wavelength effect on LC refractive indices is important for the design of direct-view displays. In Chapter 2, we derive the extended Cauchy models for describing the wavelength effect on liquid crystal refractive indices in the visible and infrared spectral regions based on the three-band model. The three-coefficient Cauchy model could be used for describing the refractive indices of liquid crystals with low, medium, and high birefringence, whereas the two-coefficient Cauchy model is more suitable for low birefringence liquid crystals. The critical value of the birefringence is deltan~0.12. Temperature is another important factor affecting the LC refractive indices. The thermal effect originated from the lamp of projection display would affect the performance of the employed liquid crystal. In Chapter 3, we derive the four-parameter and three-parameter parabolic models for describing the temperature effect on the LC refractive indices based on Vuks model and Haller equation. We validate the empirical Haller equation quantitatively. We also validate that the average refractive index of liquid crystal decreases linearly as the temperature increases. Liquid crystals exhibit a large thermal nonlinearity which is attractive for new photonic applications using photonic crystal fibers. We derive the physical models for describing the temperature gradient of the LC refractive indices, ne and no, based on the four-parameter model. We find that LC exhibits a crossover temperature To at which dno/dT is equal to zero. The physical models of the temperature gradient indicate that ne, the extraordinary refractive index, always decreases as the temperature increases since dne/dT is always negative, whereas no, the ordinary refractive index, decreases as the temperature increases when the temperature is lower than the crossover temperature (dno/dT<0 when the temperature is lower than To) and increases as the temperature increases when the temperature is higher than the crossover temperature (dno/dT>0 when the temperature is higher than To ). Measurements of LC refractive indices play an important role for validating the physical models and the device design. Liquid crystal is anisotropic and the incident linearly polarized light encounters two different refractive indices when the polarization is parallel or perpendicular to the optic axis. The measurement is more complicated than that for an isotropic medium. In Chapter 4, we use a multi-wavelength Abbe refractometer to measure the LC refractive indices in the visible light region. We measured the LC refractive indices at six wavelengths, lamda=450, 486, 546, 589, 633 and 656 nm by changing the filters. We use a circulating constant temperature bath to control the temperature of the sample. The temperature range is from 10 to 55 oC. The refractive index data measured include five low-birefringence liquid crystals, MLC-9200-000, MLC-9200-100, MLC-6608 (delta_epsilon=-4.2), MLC-6241-000, and UCF-280 (delta_epsilon=-4); four middle-birefringence liquid crystals, 5CB, 5PCH, E7, E48 and BL003; four high-birefringence liquid crystals, BL006, BL038, E44 and UCF-35, and two liquid crystals with high dno/dT at room temperature, UCF-1 and UCF-2. The refractive indices of E7 at two infrared wavelengths lamda=1.55 and 10.6 um are measured by the wedged-cell refractometer method. The UV absorption spectra of several liquid crystals, MLC-9200-000, MLC-9200-100, MLC-6608 and TL-216 are measured, too. In section 6.5, we also measure the refractive index of cured optical films of NOA65 and NOA81 using the multi-wavelength Abbe refractometer. In Chapter 5, we use the experimental data measured in Chapter 4 to validate the physical models we derived, the extended three-coefficient and two-coefficient Cauchy models, the four-parameter and three-parameter parabolic models. For the first time, we validate the Vuks model using the experimental data of liquid crystals directly. We also validate the empirical Haller equation for the LC birefringence delta_n and the linear equation for the LC average refractive index . The study of the LC refractive indices explores several new photonic applications for liquid crystals such as high temperature gradient liquid crystals, high thermal tunable liquid crystal photonic crystal fibers, the laser induced 2D+1 thermal solitons in nematic crystals, determination for the infrared refractive indices of liquid crystals, comparative study for refractive index between liquid crystals and photopolymers for polymer dispersed liquid crystal (PDLC) applications, and so on. In Chapter 6, we introduce these applications one by one. First, we formulate two novel liquid crystals, UCF-1 and UCF-2, with high dno/dT at room temperature. The dno/dT of UCF-1 is about 4X higher than that of 5CB at room temperature. Second, we infiltrate UCF-1 into the micro holes around the silica core of a section of three-rod core PCF and set up a highly thermal tunable liquid crystal photonic crystal fiber. The guided mode has an effective area of 440 ƒÝm2 with an insertion loss of less than 0.5dB. The loss is mainly attributed to coupling losses between the index-guided section and the bandgap-guided section. The thermal tuning sensitivity of the spectral position of the bandgap was measured to be 27 nm/degree around room temperature, which is 4.6 times higher than that using the commercial E7 LC mixture operated at a temperature above 50 degree C. Third, the novel liquid crystals UCF-1 and UCF-2 are preferred to trigger the laser-induced thermal solitons in nematic liquid crystal confined in a capillary because of the high positive temperature gradient at room temperature. Fourth, we extrapolate the refractive index data measured at the visible light region to the near and far infrared region basing on the extended Cauchy model and four-parameter model. The extrapolation method is validated by the experimental data measured at the visible light and infrared light regions. Knowing the LC refractive indices at the infrared region is important for some photonic devices operated in this light region. Finally, we make a completely comparative study for refractive index between two photocurable polymers (NOA65 and NOA81) and two series of Merck liquid crystals, E-series (E44, E48, and E7) and BL-series (BL038, BL003 and BL006) in order to optimize the performance of polymer dispersed liquid crystals (PDLC). Among the LC materials we studied, BL038 and E48 are good candidates for making PDLC system incorporating NOA65. The BL038 PDLC cell shows a higher contrast ratio than the E48 cell because BL038 has a better matched ordinary refractive index, higher birefringence, and similar miscibility as compared to E48. Liquid crystals having a good miscibility with polymer, matched ordinary refractive index, and higher birefringence help to improve the PDLC contrast ratio for display applications. In Chapter 7, we give a general summary for the dissertation.