  Metamaterials are nano-engineered media with designed properties beyond those
available in nature with applications in all aspects of materials science. In
particular, metamaterials have shown promise for next generation of optical
materials with electromagnetic responses that cannot be obtained from
conventional media. We review the fundamental properties of metamaterials with
hyperbolic dispersion and present the various applications where such media
offer potential for transformative impact. These artificial materials support
unique bulk electromagnetic states which can tailor light-matter interaction at
the nanoscale. We present a unified view of current research in the field of
hyperbolic metamaterials such as sub-wavelength imaging and broadband photonic
density of states engineering. The review introduces the concepts central to
the theory of hyperbolic media as well as nanofabrication and characterization
details essential to experimentalists. Finally, we outline the challenges in
the area and offer a set of directions for future work.
