Treebeard is widely considered the oldest of Eru's mortal children, he has been alive for 17,051 years and walking on middle earth for that period of time. He remained in Fangorn even after the entwives left in the 3rd age, and continued the hunt for them alongside the only other 2 remaining ents Finglas and Flandriff. However after many years searching he gave up and returned to Fangorn and gave up in his hunt for the Entwives.
Major Story Arcs
During the War of the Ring, Treebeard stumbled upon 2 hobbits: Merry and Pippin who were fleeing from an uruk-hai at the time. Treebeard killed the uruk-hai and took the 2 hobbits who he initially believed to be orcs to his home. It is here that Treebeard passed on his extensive knowledge of Fangorn and Middle Earth, and even of the awakening of the elves. He also allowed the hobbits to try the renowned Entwash. Merry and Pippin show him the destruction wrought by Treebeards' former friend and ally: Saruman.
This led to Treebeard declaring an entmoot, a bringing together of the remaining ents. After 3 days of slow deliberation the ents decided to get revenge against Saruman and destroy Orthanc. This was known as the Last March of the Ents. They completely annihilated all Saruman's forces and constructs save the tower itself in which they kept Saruman prisoner until he was slain by Grima Wormtongue.
After the 3rd Age
Following the coronation of King Elessar and the destruction of Sauron, the Ents were relieved of their duties as guardians of Orthanc. King Elessar offered them space to grow the forests and renew their race, however Treebeard lamented that though the forests may still grow, the time of their shepherds was over. We are not told when or if Treebeard died, but it is assumed he simply turned into a tree and ceased all consciousness as is customary for an Ent.