Dual frequency liquid crystal (DFLC) exhibits a positive dielectric anisotropy at low frequencies and negative dielectric anisotropy at high frequencies. The frequency where dielectric anisotropy is zero is called crossover frequency. DFLC can achieve fast rise time and fast decay time with the assistance of applied voltage. However, one drawback of DFLC is that it has dielectric heating effect when driven at a high frequency. Thus, the first part of this dissertation is to develop low crossover frequency DFLC materials. The dielectric relaxation and physical properties of some single- and double-ester compounds were investigated. Experimental results indicate that the double-ester compound exhibits a ~ 3 X lower dielectric relaxation frequencies and larger dielectric anisotropy than the single ester, but its viscosity is also higher. More generally, ten groups of dual frequency liquid crystals were compared in terms of dielectric relaxation frequency and dielectric anisotropy. The dielectric relaxation theory was discussed at last. To realize fast response time, high birefringence and low viscosity LC are required. From these two aspects, firstly four new high birefringence laterally difluoro phenyl tolane liquid crystals with a negative dielectric anisotropy were studied. These materials are used to enhance the birefringence of DFLC. They have a fairly small heat fusion enthalpy (~3000 cal/mol) which improves their solubility in a host. We dope 10 wt% of each compound into a commercial negative mixture N1 and measured their birefringence, viscoelastic constant and figure of merit. Birefringence varies very little among homologues while viscoelastic constant increases as alkyl chain length increases. Secondly, we studied the effects of six diluters for lowering the viscosity while stabilizing the vertical alignment (VA) of the laterally difluoro terphenyl host mixture at elevated temperatures. The pros and cons of each diluter are analyzed. These lateral difluoro terphenyls exhibit a high birefringence, fairly low viscosity, and modest dielectric anisotropy, but their molecular alignment in a VA cell is gradually deteriorated at elevated temperatures as their concentration increases. As a result, the device contrast ratio is decreased noticeably due to the light leakage through the crossed polarizers. Finally, liquid crystal doped with metallic nanoparticles, such as Pd, Ag, or Ag-Pd, which are protected with ligand molecules, such as nematic liquid crystal were studied. The metal nanoparticles doped LC exhibit a frequency modulation (FM) electro-optical (EO) response in the millisecond to submillisecond range together with the ordinary root-mean-square voltage response.