This dissertation delves into the challenges associated with modeling, state estimation, andparameter identification for currently prevailing lithium-ion (Li-ion) battery technologies and the emerging frontiers of lithium-sulfur (Li-S) batteries. With rapid development in electrification, Lithium-ion (Li-ion) batteries have reshaped the realms of portable electronics, electric mobility, grid storage, and renewable energy systems. The increasing scale and demand for battery systems warrant research efforts to improve battery management systems and explore alternative high-energy materials. This dissertation explores two crucial areas of focus: the development of scalable algorithms for large battery packs with heterogeneity and the design of algorithms for advanced battery chemistry, specifically Lithium-Sulfur technology. Chapters 2 to 4 focus on the challenges of Li-ion battery packs, addressing real-time power estimation in the presence of heterogeneity among individual cells. A computationally efficient and scalable algorithm for estimating the state of power (SOP) for a heterogeneous battery pack using interval prediction is first introduced in Chapter 2. In Chapter 3, the focus shifts from theoretical exploration to empirical validation, as we experimentally verify the performance of the SOP algorithm proposed in Chapter 2. In Chapter 4, heterogeneity in the cells is further explored, where uncertainty in thermal parameters is also addressed. The addition of thermal heterogeneity needed a more accurate and robust interval algorithm than originally proposed in Chapter 2. Chapter 4 enhances the performance of interval prediction using reachability analysis for mixed monotonic systems. Chapters 2 through 4 unravel the complexities of the SOP framework, elucidating its theoretical foundations, practical limitations, and the prospective transformative influence it could have on the optimization of the performance of a heterogeneous battery pack. Transitioning to emerging technologies, Chapters 5 and 6 shift the focus to Li-S batteries. Chapter 5 investigates global parameter sensitivity for a zero-dimensional Li-S battery model, addressing challenges in parameter identification crucial for battery management systems. Global sensitivity analysis is employed to understand parameter relevance and interdependence, highlighting the impact of different parameter distributions on model performance. Chapter 6 focuses on efficient modeling and state estimation algorithms for Li-S batteries, proposing a physics-informed neural network model with a moving horizon state estimator. The state estimation accuracy is compared with the extended Kalman filter. The developed model and a moving horizon estimator framework demonstrate robust state estimation accuracy under varying current profiles. In conclusion, this dissertation contributes to advancing the understanding and optimization of established and emerging battery technologies, providing valuable insights for applications ranging from automotive to grid storage.