Batteries are widely applied to the energy storage and power supply in portable electronics, transportation, power systems, communication networks, etc. They are particularly demanded in the emerging technologies of vehicle electrification and renewable energy integration for a green and sustainable society. To meet various voltage, power, and energy requirements in large-scale applications, multiple battery cells have to be connected in series and/or parallel. While battery technology has advanced significantly in the past decade, existing battery management systems (BMSs) mainly focus on state monitoring and control of battery systems packed in fixed configurations. In fixed configurations, though, the battery system performance is in principle limited by the weakest cells, which can leave large parts severely underutilized. Allowing dynamic reconfiguration of battery cells, on the other hand, allows individual and flexible manipulation of the battery system at cell, module, and pack levels, which may open up a new paradigm for battery management. Following this trend, this paper provides an overview of next-generation BMSs featuring dynamic reconfiguration. Motivated by numerous potential benefits of reconfigurable battery systems (RBSs), the hardware designs, management principles, and optimization algorithms for RBSs are sequentially and systematically discussed. Theoretical and practical challenges during the design and implementation of RBSs are highlighted in the end to stimulate future research and development.