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The natural-heterostructure concept realized in delafossites highlights theselayered oxides. While metallic, band- or Mott-insulating character may beassociated with individual layers, inter-layer coupling still plays a decisiverole. We review the correlated electronic structure of PdCoO$_2$, PdCrO$_2$ andAgCrO$_2$, showing that layer-entangled electronic states can deviate fromstandard classifications of interacting systems. This finding opens uppossibilities for materials design in a subtle Mott-critical regime.Manipulated Hidden-Mott physics, correlation-induced semimetallicity, orDirac/flat-band dispersions in a Mott background are emerging features.Together with achievements in the experimental preparation, this inaugurates anexciting research field in the arena of correlated materials.

From basic properties to the Mott design of correlated delafossites