Abstract: Due to their extraordinary electromagnetic/optical properties, zero-index media have extensive application prospects in the manipulation of electromagnetic waves, novel antenna and waveguide devices, nonlinear optics, optical absorption, electro-optical modulation, etc. In this review, we first present the classification and realization of zero-index materials. Then, we focus on their fundamental concepts and electromagnetic/optical properties, including refraction, reflection and tunneling effects of electromagnetic waves, the influence of doped defects in both two- and three-dimensions, features of anisotropic zero-index media, and the distribution of electric fields in and outside the medium. Finally, we review a variety of applications, and provide a brief summary and outlook on future studies of these materials.