In recent decades, scientists have developed the means to engineer synthetic periodic arrays with feature sizes below the wavelength of light. When such features are appropriately structured, electromagnetic radiation can be manipulated in unusual ways, resulting in optical metamaterials whose function is directly controlled through nanoscale structure. Nature, too, has adopted such techniques—for example in the unique colouring of butterfly wings—to manipulate photons as they propagate through nanoscale periodic assemblies. In this Perspective, we highlight the intriguing potential of designer structuring of electronic matter at scales at and below the electron wavelength, which affords a new range of synthetic quantum metamaterials with unconventional responses. Driven by experimental developments in stacking atomically layered heterostructures—such as mechanical pick-up/transfer assembly—atomic-scale registrations and structures can be readily tuned over distances smaller than characteristic electronic length scales (such as the electron wavelength, screening length and electron mean free path). Yet electronic metamaterials promise far richer categories of behaviour than those found in conventional optical metamaterial technologies. This is because, unlike photons, which scarcely interact with each other, electrons in subwavelength-structured metamaterials are charged and strongly interact. As a result, an enormous variety of emergent phenomena can be expected and radically new classes of interacting quantum metamaterials designed.