Various materials display a constant phase impedance, Z proportional to [i omega](-u), over a wide frequency range. In this paper, we show that this behavior is a natural consequence of charge transport in the macroscopic limit, and that in contrast to the common belief, no assumptions on the "relaxation functions" are required. Our unifying view of the constant-phase-element (CPE) is then employed for analyzing impedance spectra that were recorded during the aging of LixFePO4 cells. We find and explain a significant correlation between their capacity loss and changes in the exponent (u) of the CPE describing cathodic Li-intercalation. Changes in u with the state of charge are also discussed. CPE exponents are shown to be valuable performance indicators for Li-ion batteries. (C) The Author(s) 2015. Published by ECS. All rights reserved.