To unlock the promise of electrified transportation and smart grid, emerging advanced battery management systems (BMSs) shall play an important role in health-aware monitoring, diagnosis, and control of widely used lithium-ion (Li-ion) batteries. Sophisticated physics-based battery models incorporated in the advanced BMS can offer valuable battery internal information to achieve improved operational safety, reliability and efficiency, and to extend the lifetime of the batteries. However, developed from the fundamental electrochemical and thermodynamic principles, the rigorous physics-based models are saddled with exceedingly high cognitive and computational complexity for practical applications. This article reviews prevailing order reduction techniques of physics-based Li-ion battery models to facilitate the development of next-generation BMSs. We analyze and comparatively characterize these techniques, mainly from perspectives of model fidelity, computational efficiency, and the scope of applications. By representing many effective and flexible reduced-order models as equivalent circuits, designers and practitioners, who do not have electrochemical expertise but with knowledge of circuit theory, can readily gain insights into multi-physical dynamics as well as their coupling effects inside the batteries. In addition, recommendations are made on how to select appropriate physics-based models for various model-based applications in battery management. Finally, the prospect of physical model-enabled BMSs is discussed, including the potential challenges and future research directions.