  The natural-heterostructure concept realized in delafossites highlights these
layered oxides. While metallic, band- or Mott-insulating character may be
associated with individual layers, inter-layer coupling still plays a decisive
role. We review the correlated electronic structure of PdCoO$_2$, PdCrO$_2$ and
AgCrO$_2$, showing that layer-entangled electronic states can deviate from
standard classifications of interacting systems. This finding opens up
possibilities for materials design in a subtle Mott-critical regime.
Manipulated Hidden-Mott physics, correlation-induced semimetallicity, or
Dirac/flat-band dispersions in a Mott background are emerging features.
Together with achievements in the experimental preparation, this inaugurates an
exciting research field in the arena of correlated materials.
