This talk focuses on the multi-physics modeling and computation for electrochemical devices, such as supercapacitors and solid-state batteries. For supercapacitors, accurate characterization of entropy plays a pivotal role in capturing reversible and irreversible heating during charging/discharging cycles. First, we will present a non-isothermal electrokinetic model and corresponding entropy increasing numerical methods for the prediction of temperature oscillations observed in experiments. Numerical analysis is performed to theoretically establish the structure-preserving properties that are preserved by the numerical methods. For solid-state batteries, we present a real 2D (R2D) galvanostatic model that encodes physicochemical heterogeneity in a full battery system under realistic working conditions. Simulation results are validated against experimental data with detailed discussions.