The Return, in the Old Tongue Corenne, is the name given by the Seanchan to their invasion of the Westlands. Plans for the return date by to Luthair Hawkwing, who set out the policy to return the Westlands and avenge his father, after the news came of his death and no further news followed (TWoRJTWoT, Ch. 17). The invasion fleet consisted of thousands of ships and hundreds of thousands of people form every port and inlet of the eastern coast (TWoRJTWoT, Ch. 17). It was commanded by Lunal Galgan. Many of the people involved had no intention of returning.
Preparations for The Return were made for years before the omens said it was time to leave. They had expected to make allies who would aid them in winning the Last Battle in the name of the Empress, but instead found they had the need to conquer.
In the Old Tongue, Forerunners. The name given to the initial force of around five hundred ships, under the command of Turak.
They quickly took control of the tow of Falme on Toman Head on the Almoth Plain, hanging the Watchers over the Waves, for watching for the wrong thing and forcing all others to swear an oath to "obey, wait and serve" after which they were free to go about their business, even being allowed to leave Falme, and spread the message that they obey the Foreunners, await the Return and serve those who come home (TGH, Ch. 29). Turak set up in a large house, just outside the town (TGH, Ch. 29), where he was killed by Rand al' Thor seeking the Horn of Valere and the Ruby Dagger from Shadar Logoth (TGH, Ch. 45).
In the aftermath of Turak's death, the Seanchan battle a company of Whitecloaks under the command of Geofram Bornhald. At the same time, the Horn of Valere is blown and the Heroes of the Horn return, fighting against the Seanchan, while in the sky above, Rand al'Thor fought Ba'alzamon. When Rand was victorious, the Seanchan were driven out of Falme (TGH, Ch. 47)
The Second Invasion
After being defeated at Falme, the Seanchan regrouped in Cantorin, with Suroth taking charge, where they made plans to re-launch their invasion (TSR, Ch. 1), quickly taking control of Tarabon (ACoS, Ch. 26). From there, they were able to launch further attacks, firstly into Amadicia, where they took the Fortress of Light (ACoS, Ch. 20) before defeating Ailron and the Amadician forces (CoT, Prologue) and Altara (ACoS, Ch. 39), where they set up their control center. They were halted in their expansion eastwards by Rand al'Thor (TPoD, Ch. 24). Their attempt to expand northwards was also thwarted with the destruction of a hundred thousand strong army by Rodel Ituralde (TGS, Ch. 6). The forces of the Corenne were later subsumed into the Rhyagelle though for a time Suroth led the overall forces (KoD, Epilogue).
In the Old Tongue, "Those who come home". After the defeat at Falme, the Corenne was supposedly called off (TFoH, Ch. 32), but began again not long after, thousands of ships, with Tuon poised to take command (WH, Ch. 14). They landed at several places in the Westlands, with the intent to settle permanently, rather than return to Seanchan (ToM, Ch. 1).
The White Tower
With the Seanchan animosity towards people who can channel and especially Aes Sedai, the White Tower was viewed as a major obstacle. This was compounded by the belief that the explosion caused by Elayne attempting to unweave a gateway while fleeing from the Kin's farm was an Aes Sedai weapon. Their first response was to launch a raid on the White Tower, led by Abaldar Yulan, which succeeded in capturing almost 40 Tower initiates, with more two dozen of them being Aes Sedai including Elaida, though at great cost to the Seanchan (TGS, Epilogue). With the capture of Elaida, they were able to learn the weave for Traveling and began to plan a full scale assault (ToM, Ch. 47).
"'You overstep yourself, Galgan,' she said coldly. 'I command the Forerunners. For the time being, I command the Return. You will sign no orders without my approval."
'You commanded the Forerunners, who have been subsumed into the Return,' he replied calmly, and Suroth tasted bitterness." (Suroth and Galgan, Knife of Dreams, Epilogue).