Cascaded-bridge converters (CBCs) and modular multilevel converters (MMCs) enjoy growing popularity mostly due to modularity and scalability. Conventionally, their submodules allow only serial and bypass operation so that the use of lowvoltage components for high-voltage output becomes possible. Dually, submodule parallelization adds switched-capacitor behavior to CBCs/MMCs and has witnessed an upward trend in recent years. Salient advantages of parallel operation comprise sensorless voltage balancing, capacitance saving, current sharing, and system efficiency optimization. To capture the advancement in the field, this article reviews state-of-the-art multilevel converters with parallel connectivity, covering various submodules, macro-level circuit topologies, implementation challenges and solutions, as well as control and optimization schemes. In particular, this article derives and classifies submodules as well as macro-level topologies according to basic H-bridge, asymmetrical half-bridge, and symmetrical half-bridge submodules. On top of that, this article introduces strategies for the simplification of submodules and creation of novel topologies yet maintaining parallel connectivity. We highlight the role of graph theory on creating new analytic and synthetic methodologies for multilevel converters. In addition, this article discloses the relationship between multilevel converters with parallel connectivity and switched capacitor converters.