The charge transport through the bulk of Li 2 O 2 has been studied extensively by ex-periments and theoretical calculations. Particularly, Gerbig et al. observed the Li 2 O 2 insulating nature by impedance spectroscopy and DC conductivity measurements, showing that ionic lithium defects are the majority carriers while electronic conductivity is two order of magnitude smaller and of hole type. These results were confirmed later by Dunst et al. by means of nuclear magnetic resonance spectroscopy. Independently, Ceder and coworkers showed, using Density Functional Theory (DFT) calculations with the Heyd-Scuseria-Ernzerhof (HSE) screened hybrid functional, that holes can be self-trapped at the peroxide sites (O 2 -2 ) forming small hole polarons (O -1 2 ). Furthermore, they noted that the nonpolaronic structure, which present metallic states, has significantly higher energy than the polaronic one. Afterwards, Radin and Siegel, employing the same hybrid functional, concluded that the dominant charge carriers in bulk Li 2 O 2 are the lithium vacancies (V Li ) and hole polarons, and that the inclusion of exact exchange at some extent is essential for achieving their correct description. Li 2 O 2 surfaces have also been object of study as possible conduction paths during the operation of the cell. Previous theoretical reports have shown that the more energetically favourable surface of Li 2 O 2 under ambient conditions is metallic. These results were based on DFT calculations using functionals in the General Gradient Approximation (GGA). A metallic behaviour of the Li 2 O 2 surface would have deep consequences in the performance of the LOB since it could mitigate the electrical passivation of the cathode. Furthermore, the important role played by the Li 2 O 2 surfaces in the oxygen evolution reaction (OER) occuring during the recharge of the battery has also motivated experimental and theoretical research. Resorting to DFT calculations in the GGA approximation, Mo et al. studied the energetics and the OER for different surface orientations. Afterwards, Hummelshφj et al. investigated the electrochemical mechanism of growth and dissolution over the [1 100] Li 2 O 2 facet, the more stable one using the revised PBE functional (RPBE), analysing possible origins of the overpotential. Based on these RPBE calculations where the intermediate lithium vacancies in the OER reaction give rise to surface metallic states, they conclude that the electron transport through the Li 2 O 2 may not be a problem at the high potentials. In view of the well known self-interaction error of the GGA functional, the result of the surface metallicity was revisited 20 using the HSE correction and even the scGW method. Interestingly, the metallic behaviour that was also obtained for these corrected functionals, arises as an artifact due to a finite size effect of a small 1x1 unit cell that does not allow for surface reconstruction. In fact, calculations done later for larger supercells and proper functionals confirm that all the Li 2 O 2 surfaces are insulating and that the only charge carrier conduction path available is the diffusion of defects or through tunnelling in the case of thin films. Considering the very high computational cost of HSE, specially for simulating large supercells, the DFT+U technique was also used as an alternative to correct the underestimation of the electronic correlation characteristic of local or semilocal functionals as GGA. After this winding road towards understanding the formation and decomposition of Li 2 O 2 in the LOB, there is still some confusion in the literature regarding these fundamental issues that hinders future efforts to make progress in this promising technology and a clarification is urging.