Thirty years after its commercialization, lithium-ion rechargeable battery (LIB) has become a key technology in reducing the society’s dependence on fossil fuels and shifting towards clean, renewable energy sources. Despite tremendous progress, Li- ion batteries still face significant barriers to their wide adoption in electrical vehicles and electric grid storage. Fundamental understanding of the physical phenomena in battery systems at all length scales, including the mesoscopic level, is essential to enable further technological advancement in cost reduction, energy density improvement and cycle life extension. Many battery electrode materials undergo first-order phase transformations upon battery cycling, which frequently control the lithium intercalation kinetics and significantly impact on the degradation process. Extensive research reveals that phase transformations in intercalation compounds exhibit distinct characteristics from other types of material systems, many of which are still under debate and remain to be fully understood. A clear elucidation of these unique features has important implications for discovering and designing better battery materials. In this thesis, computational modeling is applied to investigate the mesoscale phase transformation kinetics in lithium battery electrodes, using lithium iron phosphate olivine (LiFePO4) cathode as the model system. Phase-field models are developed and implemented to simulate the concurrent lithium transport, phase transition and stress evolution in LiFePO4 during (de)lithiation, which generates several significant findings including: 1) The coherency stress between the LiFePO4 and FePO4 phases induces the morphological instability in the phase growth front and results in non-uniform intercalation in single crystalline particles. 2) Phase transition in LiFePO4 secondary particles exhibits one-dimensional growth behavior, which can be attributed to the anisotropic stress generated by the LiFePO4 /FePO4 lattice misfit and the strong elastic interaction between primary particles, 3) Antisite defects have the surprising effect of accelerating the phase growth kinetics by increasing the surface area of active Li intercalation during battery charge/discharge. Due to high computational cost, simulating microstructure evolution in battery systems is still limited in spatiotemporal scales. To address this challenge, we develop a data-driven modeling approach by replacing PDE-based simulations with machine learning algorithms based on convolutional recurrent neural networks (ConvRNN). The ConvRNN model is demonstrated to accelerate predictions up to 1000 folds for several classical microstructure evolution examples. It offers a promising alternative for efficient battery simulation at the mesoscale level in the future.