Photonic crystals and metamaterials have emerged as the most widely used artificial media for controlling light-matter interaction in solid state systems. The former relies on Bragg scattering from wavelength sized periodic modulation in the dielectric environment while the latter has sub-wavelength sized sub-structures that are designed to give an effective medium response. Here we report a new class of artificial photonic media: “photonics hypercrystals” for control of light matter interaction. Hypercrystals are distinct from photonic crystals, as both material scales involved - the hypercrystal period and the unit cells of its material components - are sub-wavelength. And they are also not metamaterials, as their electromagnetic response is qualitatively different from the expected averaged behavior. This fundamental difference results in a number of nontrivial electromagnetic properties of the hypercrystals, that can be observed in experiment and even lead to practical devices - from broadband enhancement of spontaneous emission and light out-coupling which has never to date been demonstrated simultaneously in either metamaterials or photonic crystals, to Dirac physics and singularities in sub-wavelength sized lattice. Specifically, we demonstrate enhanced spontaneous emission rate (x20) and light out-coupling (x100) from a two-dimensional metal-dielectric hypercrystal embedded with quantum dots. Such designer photonic media with complete control over the optical properties provide a new platform for broadband control of light-matter interaction.