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We present the results of novel, time-resolved, in situ HRTEM observations, molecular dynamics (MD) simulations, and disconnection theory that elucidate the mechanism by which the motion of grain boundaries (GBs) in polycrystalline materials are coupled through disconnection motion/reactions at/adjacent to GB triple junctions (TJs). We focus on TJs composed of a pair of coherent twin boundaries (CTBs) and a Σ9 GB. As for all GBs, disconnection theory implies that multiple modes/local mechanisms for CTB migration are possible and that the mode selection is affected by the nature of the driving force for migration. While we observe (HRTEM and MD) CTB migration through the motion of pure steps driven by chemical potential jump, other experimental observations (and our simulations) show that stress-driven CTB migration occurs through the motion of disconnections with a non-zero Burgers vector; these are pure-step and twinning-partial CTB migration mechanisms. Our experimental observations and simulations demonstrate that the motion of a GB drags its delimiting TJ and may force the motion of the other GBs meeting at the TJ. Our experiments and simulations focus on two types of TJs composed of a pair of CTBs and a Σ9 GB; a 107° TJ readily migrates while a 70° TJ is immobile (experiment, simulation) in agreement with our disconnection theory even though the intrinsic mobilities of the constituent GBs do not depend on TJ-type. We also demonstrate that disconnections may be formed at TJs (chemical potential jump/stress driven) and at GB/free surface junctions (stress-driven).