Abstract: The design and operation of rechargeable batteries is predicated on directing flows of mass, charge, and energy across multiple interfaces. Understanding such flows requires knowledge of atomistic and mesoscale diffusion pathways and the coupling of ion transport with electron conduction and stress gradients across length scales. Using multiple polymorphs of V2O5 as model systems, I will discuss our efforts to develop an Angstrom-level view of diffusion pathways using single-crystal X-ray diffraction studies of topochemical transformations. I will further discuss the accumulative results of atomic scale inhomogeneities at single-particle and particle ensemble levels based on scanning transmission X-ray microscopy and X-ray ptychography measurements of lithiation inhomogeneities and stress gradients. The mitigation of diffusion impediments will be discussed with reference to two distinct approaches: (a) utilization of Riemann manifolds as a geometric design principle for electrode architectures and (b) the atomistic design of polymorphs with well-defined diffusion pathways that provide frustrated coordination.  Finally, I will discuss the role of chemical substitution and the extent to which it can be considered a proxy for stress modification.