The design and operation of rechargeable batteries is predicated on orchestrating flows of mass, charge, and energy across multiple interfaces. I will discuss our efforts to develop an Angstrom-level view of diffusion pathways using a combination of single-crystal X-ray diffraction and density functional theory calculations. I will emphasize mitigation of diffusion impediments through: (a) utilization of Riemannian 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. The latter approach, involving navigating metastable phase space, holds opportunities for non-equilibrium structural motifs and ultimately for the realization of novel function. Using binary, ternary, and quaternary oxides of vanadium, as illustrative examples where topochemical synthetic strategies have unveiled novel polymorphs, I will highlight the tunability of electronic structure, the potential richness of energy landscapes, and the implications for discovering promising intercalation hosts for both multivalent and anion batteries.