<p>The electromagnetic response of materials serves as the foundation for a broad range of vital applications, from imaging, to sensing, to classical and quantum communications. Here we demonstrate, theoretically and experimentally, a fundamentally new regime of electromagnetic material response originating from inherent material nonlocality. We show that by structuring materials on the intrinsic scale of this nonlocal response, it becomes possible to alter the electromagnetics of the composite, revealing the inherent nonlocal behavior of the constituent components. These intrinsically nonlocal metamaterials exhibit strong intrinsic (as opposed to effective) nonlocality, easily detectable at room temperatures, in realistic (lossy), macroscopic materials. Intrinsically nonlocal metamaterials open a new design space for electromagnetic composites, beyond photonic crystals, metasurfaces, and effective medium composites. This allows the control of electromagnetic fields at a deep subwavelength scale, revealing a new dimension for control of light-matter interactions.</p>