The delafossites are a series of layered compounds with triangular lattices similar to that of NaCoO2 but with a different stacking sequence along the c axis. They are host to intriguing magnetic insulators and semimetals, as well as metals such as PdCoO2, PtCoO2, PdCrO2 and PdRhO2. The properties of these metals are remarkable. Although they are strongly two-dimensional, their room temperature electrical conductivity is higher per carrier than that of any elemental metal, and PdCoO2 crystals can have a low temperature resistivity of only a few nΩcm, corresponding to mean free paths of tens of microns. On the one hand, our group is attempting to accept this huge conductivity and profit from it, for example by investigating whether we can enter the hydrodynamic regime of electronic transport. On the other hand we are trying to understand why the conductivity is so high, combining spectroscopic properties and electronic structure calculations. I will report on our progress on both fronts.