The icosahedral (i-) AlPdRe is the most resistive quasicrystalline alloy discovered so far. Resistiv-ities (ρ) of 1Ωcm at 4K and correlated resistance ratios (RRR = ρ4K /ρ300K) of more than 200 are observed in polycrystalline samples. These values are two orders of magnitude larger than for the isomorphous i-AlPdMn phase. We discuss here the controversial microscopic origin of the i-AlPdRe alloy electrical specificity. It has been proposed that the high resistivity values are due to extrinsic parameters, such as secondary phases or oxygen contamination. From comprehensive measurements and data from the literature including electronic transport correlated with micro structural and mi-cro chemical analysis, we show that on the contrary there is mounting evidence in support of an origin intrinsic to the i-phase. Similarly to the other quasicrystalline alloys, the electrical resistivity of the i-AlPdRe samples depends critically on minute changes in the structural quality and chemical composition. The low resistivity in i-AlPdRe single-grains compared to polycrystaline samples can be explained by difference in chemical composition, heterogeneity and thermal treatment.