Eomer and his sister Eowyn came under the care of their uncle King Theoden when their parents died and came to live with them in the realm of Rohan. Eomer was captain of the guard to his uncle's riders and was well respected amongst the Men for his faithful service to his country and people.
The Two Towers
In The Two Towers, Éomer and his men hunted down the Uruk-hai that had taken Meriadoc Brandybuck and Peregrin Took and slaughtered them all in the dead of Night. Luckily, Merry and Pippin escaped into Fangorn Forest and were unnoticed by Eomer and his party. He later encountered Aragorn, Legolas and Gimli of the Fellowship of the Ring, searching for their friends. Despite Éomer saying there were no survivors, he still gave them two horses to find their missing friends. Éomer returned home and informed his uncle of letting the three hunters go, which was seen as a violation of the King's law. Under the poisonous advice of Grima Wormtongue, Theoden had Éomer imprisoned, which led Éomer to the conclusion that his uncle was under the influence of Saruman.
When Grima was discovered for being a traitor when Theoden was healed by Gandalf and restored him to health and vitality. Éomer was freed and named heir to Théoden's throne before they departed to the Hornburg and left Éowyn in charge of the kingdom.
At the battle of the Hornburg, Éomer and his éored drove the orcs and Dunlendings of Saruman to the walls of the Glittering Caves and had them slaughtered. He built defense of the gate where he, Aragorn and a small band of men left through a small door at the Hornburg's side. They led an assault on Saruman's Uruk-hai, who had attempted to break in. They were forced to retreat, where Eomer was jumped on by several orcs but he was miraculously saved by Gimli. The battle ended in victorious for the free people of Middle-earth
He rode with Theoden, Aragorn, Gandalf, Legolas and Gimli to Isengard, where they were greeted by Merry and Pippin, who were celebrating their recent victory against Saruman, who has now been imprisoned with Wormtongue. Treebeard and his fellow Ents would be there to guard both wizard and servant.
The Return of the King
Now knowing that Sauron was going to strike Gondor, Eomer helped his uncle rally six thousand soldiers before going to war. Eomer fought gallantly in the battle. However, Theoden was fatally crushed by his horse, Snowmane, after beign thrown by the Witch-king. When the battle was over, Eomer saw his sister next to the body of their uncle and was driven to temporary madness at seeing his younger sister apparently dead. It renewed his fury for Mordor, but Eowyn was still alive, but barely due to being poisoned by the black breath. Eomer attended to his siter in the House of Healings, where she was healed by Aragorn. Aragorn said that, as broken as Eowyn's heart was over Aragorn, the love for her brother was realt o her and gave her more potent reason to live.
Upon his uncle's death, Eomer was the new king of Rohan. He was part of the Last Debate (which was to decide the fate of the battles) and the battle at the Black Gate. During Aragorn's coronation, Éomer and Aragorn renewed the Oath of Eorl, ensuring everlasting friendship between both Rohan and Gondor.
After the War of the Ring
While in Gondor after the War of the Ring, Éomer met Lothiriel who he married. Eomer and Lothiriel were king and queen of Rohan and they had a son named Elfwine.