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The unique features of flexoelectric and dielectric effects are investigated, and exploited for a variety of functions, in a wide range of helicoidal liquid crystal systems, including non-chiral, cholesteric and blue phases. Electrooptic techniques are developed to measure flexoelectric parameters in non-chiral and cholesteric liquid crystals using twisted nematic and Grandjean geometries respectively. A crystal rotation method, and using a lock-in amplifier, is used to enable the measurement of a very small e/K of 0.011 C/N^-1m^-1. Enhancement in chiral-flexoelectric switching is demonstrated theoretically in liquid crystals with negative dielectric anisotropy and in systems in which the pitch is constrained to be other than the natural pitch. A methodological framework for inducing stable Uniform Lying Helix alignment is developed based on weak homeotropic alignment conditions and a method to bias the helicoidal axis orientation; a series of approaches within this framework are demonstrated, including nano-grooved interfaces, periodic boundaries conditions, in-plane fields, and mould-templated micro-channels. The latter approach is potentially commercially viable for sub-millisecond electrooptic technology. The contribution to a cholesteric material's effective dielectric permittivity of flexoelectric polarization is formulated, and an ability to switch a cholesteric between Grandjean and lying-helix configurations based on the dispersion in the flexoelectric polarization and resultant relaxation in dielectric properties is demonstrated. The flexoelectric contribution to dielectric permittivity is exploited to enable switching in bistable reflective displays and alignment of the Uniform Lying Helix. The existence of a flexoelectric contribution to Kerr switching in blue phases is demonstrated, and a semi-empirical model for the effect is developed. The effect is the first known example of a non-polar flexoelectrooptic effect. Independent flexoelectric and dielectric contributions to Kerr switching in blue phases are measured experimentally by measuring the induced birefringence as a function of driving frequency in flexoelectric- and dielectric-dominated wide-temperature-range blue phase materials.

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