The Galactic Civil War happened. Then it continued to happen even though it was really over because the losing side just couldn't deal with it. The only part that anyone cares about was the part from the Battle of Yavin through the Battle of Endor, which served as really nice bookends to the burgeoning career of the worst genocidal maniac the galaxy had ever known. When Endor happened, the Sith were destroyed, their gigantic planet smashing Balls were exploded, the remnants of imperial troops scattered, and the Republican Senate restored.
Nevertheless, for decades, ex-imperials continued to hold rallies and wave annoying flags, saying things like "The Empire will rise again!" while they carefully plotted to reverse what was known as "The War of Jedi Aggression". They did this by putting on costumes and recreating the battles they lost, but they usually got bored and went back to spending their free time watching podraces, competing in banjo duels, having sex with their cousins, and shopping for camouflage pants at Wal*Mart They continued to insist that they were robbed, and they would have won the War, "were it not for those pesky kids and their droids!"
This continued on for decades. The Alliance was not impressed, and in celebration of their victory, they installed indoor plumbing in their homes.