Liquid crystal display is now the dominant technology for information displays, which is widely used in small size displays, such as calculators, mobile phones, and digital cameras; medium size displays, such as laptops and desktop monitors; large size displays, such as direct-view TV and projection TV. Although traditional liquid crystals, such as nematic liquid crystals and cholesteric liquid crystals, exhibit fast response to electric field, higher quality displays are pursued along with the improvement of the people's living standards. It requires liquid crystals of faster response to satisfy the dynamic display of high resolution. This paper systematically summarizes the factors affecting the LC response, and emphasizes several kinds of new liquid crystals of fast responsiveness, such as polymer stabilized blue phase liquid crystal, ferroelectric liquid crystal, ferroelectric nematic liquid crystal and electric modulation of order parameters. Finally, we rationally anticipate the promising applications of fast response liquid crystals in displays and photonic devices.