The development of the next generation of rechargeable batteries and their consequent market penetration, require a rational guide for the optimization of the balance between the intrinsic capacity of the used storage materials, their statistical utilization in the composite electrodes and the macroscopic cell design. Computational multiscale modeling emerges nowadays as a powerful tool for building such a rational guide through the in silico representation of complex processes involving electrochemistry and species transport in operando conditions [1-3]. In this contribution we discuss our most recent progresses on the development of a novel integrative multiscale modeling platform devoted to understand the impact of the electrodes mesostructure on the electrochemical response of rechargeable batteries. The platform is supported on a combination of deterministic (continuum) and stochastic (Kinetic Monte Carlo) models resolving detailed electrochemistry and reactants/charge transport [4-6]. It allows capturing, with three-dimensional resolution, the impact of properties such as active material particles percolation, pore size distributions and pores interconnectivity, on the discharge cell performance (Figure). The flexibility of the approach is illustrated here through the investigation of hierarchical carbons as positive host electrode material in lithium-sulfur [7] and lithium-O2 batteries. In general, simulations reveal heterogeneities on the spatial location of electrochemical activity and nucleation centers with a strong dependence on the carbon mesostructural properties. Specific similarities and differencies between the two illustrated applications are discussed and possible ways for optimizing the electrodes performance are suggested. [1] Physical Multiscale Modeling and Numerical Simulation of Electrochemical Devices for Energy Conversion and Storage: From Theory to Engineering to Practice. A.A. Franco, M.L. Doublet, W.G. Bessler (Eds.), Springer (2015). [2] A.A. Franco, RSC Advances, 3 (32) (2013) 13027. [3] A.A. Franco (Ed.), Rechargeable Lithium Batteries: From Fundamentals to Applications, Woodhead/Elsevier Science (2015). [4] G. Blanquer, Y. Yin, M.A. Quiroga, A.A. Franco, J. Electrochem. Soc., 163 (3) (2016) A329. [5] K. H. Xue, E. McTurk, L. Johnson, P.G. Bruce, A.A. Franco, J. Electrochem. Soc., 162 (4) (2015) A614. [6] M. Quiroga, K.H. Xue, T.K. Nguyen, H. Huang, M. Tulodziecki, A.A. Franco, J. Electrochem. Soc., 161(8) (2014) E3302. [7] K.H. Xue, V. Thangavel, Y. Mammeri, M.A. Quiroga, C. Guery, P. Johansson, M. Morcrette, A.A. Franco, in preparation (2015). Figure 1