In this paper, we present calculations of some of the key physical properties of microstructures of electrodes and separators present in lithium-ion batteries with porous electrode architectures. We analyze three-dimensional models of public domain real commercial porous anodes, cathodes and polyethylene (PE) separator, in order to characterize some of their microstructural properties. First, a pore space analysis of the binarized microstructure reveals the location and distribution of pores of various sizes, the overall porosity distribution and connectivity. Next, diffusion simulations using a random-walk method are performed to compute and accurately validate in-plane and through-plane effective transport coefficients and tortuosities, for different electrodes and calendaring levels. Single phase fluid flow simulations are performed using a commercial Lattice Boltzmann Method (LBM) solver to accurately validate the permeability of the microstructures. Next, multi-phase fluid flow simulations are done using this LBM solver to simulate the electrolyte in-filling process for various solvents. We predict that in-filling process may result in residual gas bubbles, which effect is shown in subsequent diffusion simulations to reduce the effective transport. The calculated McMillan numbers after in-filling show good agreement with experimental results. Next, we simulate the mechanical deformation of these microstructures under compressive strain using a finite element analysis (FEA) solver. This work illustrates how the use of multi-physics simulation tools can help to design these microstructures to satisfy the mechanical and electrochemical properties required of them.