Hyperbolic metamaterials are anisotropic materials that exhibit unique electromagnetic properties due to their singular photonic density of states. Originally introduced to overcome the diffraction limit in optical imaging, they have since shown potential in various applications such as super-resolution imaging, stealth technology, quantum electrodynamics, thermal hyperconductivity, and superconductivity. These materials typically consist of layered metal-dielectric or metal wire structures, and their properties arise from the opposite signs of their dielectric permittivities in different directions. This leads to hyperbolic dispersion laws, enabling infinite photonic density of states and super-resolution imaging. The density of states in hyperbolic metamaterials can be enhanced by factors of 10^3 to 10^5, leading to significant improvements in radiative transfer rates. The hyperlens, a type of hyperbolic metamaterial, allows for super-resolution imaging by utilizing the unique dispersion properties of these materials. Experimental results have demonstrated the effectiveness of hyperbolic metamaterials in achieving subwavelength resolution. Additionally, hyperbolic metamaterials have shown potential in radiative heat transfer, with thermal hyperconductivity surpassing conventional materials. Photonic hypercrystals, which combine the properties of hyperbolic metamaterials and photonic crystals, have been demonstrated to exhibit enhanced sensitivity in sensing applications. Superconducting hyperbolic metamaterials have also been explored, with their properties influenced by the effective dielectric response function. These materials show promise in increasing the critical temperature of superconductors through dielectric response engineering. Overall, hyperbolic metamaterials offer a wide range of applications in optical imaging, sensing, and thermal management due to their unique electromagnetic properties.Hyperbolic metamaterials are anisotropic materials that exhibit unique electromagnetic properties due to their singular photonic density of states. Originally introduced to overcome the diffraction limit in optical imaging, they have since shown potential in various applications such as super-resolution imaging, stealth technology, quantum electrodynamics, thermal hyperconductivity, and superconductivity. These materials typically consist of layered metal-dielectric or metal wire structures, and their properties arise from the opposite signs of their dielectric permittivities in different directions. This leads to hyperbolic dispersion laws, enabling infinite photonic density of states and super-resolution imaging. The density of states in hyperbolic metamaterials can be enhanced by factors of 10^3 to 10^5, leading to significant improvements in radiative transfer rates. The hyperlens, a type of hyperbolic metamaterial, allows for super-resolution imaging by utilizing the unique dispersion properties of these materials. Experimental results have demonstrated the effectiveness of hyperbolic metamaterials in achieving subwavelength resolution. Additionally, hyperbolic metamaterials have shown potential in radiative heat transfer, with thermal hyperconductivity surpassing conventional materials. Photonic hypercrystals, which combine the properties of hyperbolic metamaterials and photonic crystals, have been demonstrated to exhibit enhanced sensitivity in sensing applications. Superconducting hyperbolic metamaterials have also been explored, with their properties influenced by the effective dielectric response function. These materials show promise in increasing the critical temperature of superconductors through dielectric response engineering. Overall, hyperbolic metamaterials offer a wide range of applications in optical imaging, sensing, and thermal management due to their unique electromagnetic properties.