Combining the power and possibilities of heterostructure engineering with the collective and emergent properties of quantum materials, quantum-matter heterostructures open a new arena of solid-state physics. Here we provide a review of interfaces and heterostructures made of quantum matter. Unique electronic states can be engineered in these structures, giving rise to unforeseeable opportunities for scientific discovery and potential applications. We discuss the present status of this nascent field of quantum-matter heterostructures and its limitations, perspectives, and challenges.

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