An entirely new functional material named photonic fractal has been developed. It can strongly localize electromagnetic waves in a dielectric fractal cube called Menger sponge without reflection and transmission. The wavelength and frequency of the localized mode can be predicted using a simple equation associated with the fractal geometry and the spatially averaged dielectric constant of the Menger sponge structure. A wide variety of applications to communication, information, energy, sensing, medical care, and other fields are considered. Design and fabrication of Menger sponge fractals with epoxy resin and ceramics, their electromagnetic wave responses, integration of photonic fractals as well as potential applications are reported.