This paper investigates the theories and applications of power flow control in multi-active-bridge (MAB) power converters. Many emerging applications including differential power processing, low voltage power delivery in smart homes, multi-cell battery balancers, and photovoltaic energy systems comprise sophisticated power flow across multiple dc voltage ports. Connecting many dc voltage ports together with a MAB converter reduces the power conversion stress, improves the efficiency and enhances the power density. Fundamentally, the advantages of a MAB design come from merging many standalone magnetic components with simple functions into one single magnetic component that performs sophisticated functions. Three control strategies for MAB converters, including phase-shift (PS) control, time-sharing (TS) control, and hybrid phase-shift and time-sharing (PSTS) control are developed to regulate the voltage and precisely control the power flow. A four-port MAB converter prototype designed for low voltage power delivery applications in future smart homes has been built and tested to compare the performance of the three control methods and verify the effectiveness of the proposed architecture.