High-level supervisory control systems require information about the internal states of an energy storage system, such as the state of charge and power capability. These quantities are not directly measureable, so models are necessary to estimate this information from the measured voltage, current and temperature. Empirical models often lack accuracy, particularly under extreme operating conditions. However, models that are closer to the physics are mathematically complex and computationally expensive, which is prohibitive for on-board applications. Our efforts here span a wide range of issues, from parameter estimation and identifiability of models, to model order reduction and observer design.