Here we present new models to capture the coupling between intercalation chemistry and mechanics arising from stacking-sequence changes and Jahn-Teller distortions. This includes first-principles simulations and mesoscale models to elucidate the thermodynamics and kinetics of stacking sequence changes, as well as analyses of how these transformations might result in irreversible changes to microstructure. Regarding the mechanics of Jahn-Teller distortions, we have developed anharmonic vibrational models to explore the transition from a collective distortion to a dynamic one in layered materials such as lithium nickel and manganese oxides (as well as their sodium analogues). Numerical simulations reveal how the interplay between the shape of the Jahn-Teller energy landscape and rigidity of the crystal impact the local structure and thermodynamic properties of the dynamically distorted phase.