  The electronic transport properties of the delafossite oxides ABO$_2$ are
usually understood in terms of two well separated entities, namely, the
triangular A$^+$ and (BO$_2$)$^-$ layers. Here we review several cases among
this extensive family of materials where the transport depends on the
interlayer coupling and displays unconventional properties. We review the doped
thermoelectrics based on CuRhO$_2$ and CuCrO$_2$, which show a high-temperature
recovery of Fermi-liquid transport exponents, as well as the highly anisotropic
metals PdCoO$_2$, PtCoO$_2$ and PdCrO$_2$ where the sheer simplicity of the
Fermi surface leads to unconventional transport. We present some of the
theoretical tools that have been used to investigate these transport properties
and review what can and cannot be learned from the extensive set of electronic
structure calculations that have been performed.
