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Building on discoveries in graphene and two-dimensional (2D) transition metaldichalcogenides, van der Waals (VdW) layered heterostructures - stacks of such2D materials - are being extensively explored with resulting new discoveries ofnovel electronic and magnetic properties in the ultrathin limit. Here we reviewa class of naturally occurring heterostructures - so called misfits - thatcombine disparate VdW layers with complex stacking. Exhibiting remarkablestructural complexity and diversity of phenomena, misfits provide a platform onwhich to systematically explore the energetics and local bonding constraints ofheterostructures and how they can be used to engineer novel quantum fabrics,electronic responsiveness, and magnetic phenomena. Like traditional classes oflayered materials, they are often exfoliatable and thus also incorporatable asunits in manually or robotically stacked heterostructures. Here we review theknown classes of misfit structures, the tools for their single crystal and thinfilm synthesis, the physical properties they exhibit, and computational andcharacterization tools that are unraveling their complexity. Directions forfuture research are also discussed.

Misfit Layered Compounds: Unique, Tunable Heterostructured Materials with Untapped Properties