We present the results of experimental and theoretical studies that demonstrate the feasibility of realizing electro-optical switching, frequency filtering and negative index of refraction. In liquid crystal infiltrated TiO2 inverse opal 3-D photonic crystals, we observed a sizeable electrical tuning of the Bragg reflection peak. In frequency selective structures with a liquid crystal over-layer, the tuning range can be as wide as 380 nm, operational throughout the entire visible - far infrared spectra range. Furthermore, some of the structures can be designed to exhibit a negative index of refraction property over a predetermined frequency interval.