After his father was killed battling orcs, Aragorn was sent to live in Rivendell with his mother, Gilraen. Around his twentieth year, as he was walking in the woods singing a part of the Lay of Lúthien, he witnessed the beauty of Arwen for the first time, clad in a mantle of silver and blue. Mistaking her for Lúthien, he called to her by that name, and, from that moment on, loved only her. Gilraen warned Aragorn of the folly of his love for Arwen, a high-born elf such as she was. Aragorn soon left Imaldis, and for thirty years fought against Sauron on whatever front which was deemed necessary.
In his forty-ninth year of life, after years of strife and toil, he wished, once again, to be at peace. He came into Loren, not knowing that Arwen also was there, and stayed with her for a season. "And thus it was that Arwen first beheld him again after their long parting; and as he came walking towards her under the trees of Caras Galadhon laden with flowers of gold, her choice was made and her doom appointed." On Cerin Amroth, in the midst of Lórien they plighted their troth looking toward the shadow of the east and the twilight of the west.
After The War of the Ring, Arwen and Aragorn were married and spent six-score years in bliss. As Aragorn felt his life drawing to a close, he came to Arwen, saying, "In sorrow we must go, but not in despair. Behold! we are not bound for ever to the circles of the world, and beyond them is more than memory."
After he passed from the world in the House of the Kings, she bid farewell to Eldarion and her daughters, and went out of Minas Tirith to Lórien and, "dwelt there alone under the fading trees until winter came." Sometime before the Spring she laid herself down upon Cerin Amroth, and there she would lie until the world's ending.
Note:
Sorry it was so short. This story is more about Rhiannon and her expectations then Arwen. Know that this is not the only chapter you will see Arwen again.