"In two domains the bliss and beauty of the Elves remained still undiminished while that Age endured: in Imladris; and in Lothlórien."
The Elves of Middle-earth are the First of the Children of Illuvatar. They do not physically age and don't suffer from illness, although they can be killed through violence. The race of Elves declined throughout the Second and Third Ages of Middle-earth due to wars with Sauron and departure to Valinor. By the War of the Ring, elves mainly lived in four areas of Middle-earth, although a few (the Avari) lived in the far east. The Elves of Lindon lived in the Grey Havens by the Ered Luin; it was from here that ships left Middle-earth to carry elves (and the Ringbearers) to Valinor. Elrond established an Elven outpost at Rivendell (Imladris). This became a refuge for High Elves, a sanctuary for travellers and a home for many young Heirs of Isildur. Lothlorien was an elven forest east of the Misty Mountains and was home to the Silvan Elves. It was ruled by Lord Celeborn and Lady Galadriel (who used the Elven Ring, Nenya, to keep the land pure). Finally, Mirkwood (previously Greenwood the Great) was a massive forest east of the Misty Mountains. The south of the forest was corrupted by the Necromancer of Dol Guldur. However, the north was a home to the Wood Elves who were ruled by King Thranduil in the Third Age.