Multi-port DC-DC converters are a promising solution for a wide range of applications involving multiple DC sources, storage elements, and loads. Multi-active bridge (MAB) converters have attracted the interest of researchers over the past two decades due to their potential advantages such as high power density, high transfer ratio, and galvanic isolation, for example, compared to other solutions. However, the coupled power flow nature of MAB converters makes their control implementation difficult, and due to the multi-input, multi-output (MIMO) structure of their control systems, a decoupling control strategy must be designed. Various control and topology-level strategies are proposed to mitigate the coupling effect. This paper discusses the operating principles, applications, methods for analyzing power flow, advanced modulation techniques, and small signal modelling of the MAB converter. Having explained the origin of cross-coupling, the existing power flow decoupling methods are reviewed, categorized, and compared in terms of effectiveness and implementation complexity.