A review is given of recent theoretical and experimental studies on the liquid crystal (LC) infiltration of 3D photonic crystal (PC) structures so as to obtain tunable Bragg reflection and transmission characteristics. It is shown that large-pore and non-close-packed inverse opals formed by sintering, or by a multiple-layer conformal deposition technique, provide a simple and effective dielectric scaffold for liquid crystal infiltration. The dynamic optical properties are strongly dependent on the scaffold structure and the dielectric contrast between the scaffold and the LC. Experimental structures were fabricated using precise, conformal, low temperature atomic layer depositions of Al2O3 and TiO2 to create inverse opals and non-close-packed inverse opals, which were subsequently infiltrated with the nematic liquid crystals 5CB and MLC2048. The dependence of the visible/infrared reflectance and transmittance were investigated as functions of applied electric field amplitude and frequency for applications in optical modulation and switching.