High temperature interface superconductivity

•This review article covers the topic of high temperature interface superconductivity.•New materials and techniques used for achieving interface superconductivity are discussed.•We emphasize the role played by the differences in structure and electronic properties at the interface with respect to the bulk of the constituents. High-Tc superconductivity at interfaces has a history of more than a couple of decades. In this review we focus our attention on copper-oxide based heterostructures and multi-layers. We first discuss the technique, atomic layer-by-layer molecular beam epitaxy (ALL-MBE) engineering, that enabled High-Tc Interface Superconductivity (HT-IS), and the challenges associated with the realization of high quality interfaces. Then we turn our attention to the experiments which shed light on the structure and properties of interfacial layers, allowing comparison to those of single-phase films and bulk crystals. Both ‘passive’ hetero-structures as well as surface-induced effects by external gating are discussed. We conclude by comparing HT-IS in cuprates and in other classes of materials, especially Fe-based superconductors, and by examining the grand challenges currently laying ahead for the field.