Recently, multilevel converters (MLCs) have gained significant attention for stationary applications, including static compensators, industrial drives, and utility-grid interfaces for renewable energy sources. Compared to two-level voltage-source inverters (VSI) MLCs feature high-quality AC voltage with reduced harmonic content despite the lower switching frequency of the semiconductor devices. On the DC side, MLCs can integrate multiple isolated/non-isolated battery modules instead of a single battery pack. This helps to keep the system in service in case of a malfunction of one or more battery modules, as well as active balancing among the modules, a feature not possible with two-level VSI. In general, MLCs can be classified into two types: (i) two-port MLCs, which provide a single interface to connect with the battery pack, and (ii) multiport MLCs, which provide multiple interfaces to allow connection at the module or cell level. The classical topologies of both MLC types (e.g., neutral point clamped, flying capacitor, cascaded bridge) face limitations due to the high switch count. Consequently, many hybrid and reduced-switch topologies are reported in the literature. This paper presents a critical overview of both classical and recently reported MLC topologies and offers a better insight of MLC operation for grid-connected and standalone applications. In addition, the analysis thoroughly assesses various high-level control and modulation strategies while considering active balancing among the battery modules. Other salient features such as balancing speed during offtake/grid-injection mode and fault-ride-through capability are also incorporated. In conclusion, the key findings are summarized for a better understanding of the present and future integration of battery systems in stationary applications.