Circles of the World
"Circles of the World" was a general term that seems to refer to the boundaries between the World and the Outer Void, though its usage is vague and does not seem to be completely consistent.
In some of its uses, it appears to be a completely inclusive term, describing the entirety of the World and its surrounding seas and airs, and explicitly including the Undying Lands of Aman. The region beyond the Circles is then the place where Ilúvatar dwells (presumably with those of the Ainur who did not descend into Arda). Maedhros fears that because of the Oath of Fëanor, their may no longer be able to "reach to Ilúvatar beyond the Circles of the World".
It is the fate of Men to pass out of the Circles of the World after death. Aragorn refers to the Circles of the World to Arwen Undómiel at his death, saying that they were not bound forever to the Circles of the World, and would meet again. A similar phrase occurs in the story of Beren Erchamion and Lúthien Tinúviel, where it is said their paths "led together beyond the confines of the world".
Further to the Downfall of Númenor, the term apparently took a more narrow meaning. After the Changing of the World, and the taking away of Aman, the lands of the Uttermost West are said to be no longer within the Circles of the World, though they are clearly still part of the World in some sense. After this point, it seems that the Circles of the World are simply the boundaries of the Mortal Lands of Middle-earth. Notably, the choice is eventually offered to the children of Elrond, either to become mortal or "to pass with him from the circle of the world". More generally, Elves, leaving Middle-earth, are said to "dwell now beyond the circles of the world". 
Jason Fisher identifies possible sources for this phrase in the Norse kringla heimsins ("circle of the world" in the Heimskringla), the Latin orbis terrarum (notably found in the Vulgate, and particularly in the Book of Wisdom), and the design of medieval T-O maps such as the mappa mundi of Hereford (where the circular world-map is surrounded by the letters M, O, R and S, spelling out "death" in Latin).
- Beyond the Circles of the World: Death and the West in Tolkien's Middle Earth Legendarium by Rebekah Hunt
- J.R.R. Tolkien, Christopher Tolkien (ed.), The Silmarillion, "Quenta Silmarillion: Of the Voyage of Eärendil and the War of Wrath"
- J.R.R. Tolkien, The Lord of the Rings, Appendix A, "The Númenorean Kings", "The Tale of Aragorn and Arwen"
- J.R.R. Tolkien, Christopher Tolkien (ed.), The Silmarillion, "Quenta Silmarillion: Of Beren and Lúthien"
- J.R.R. Tolkien, Christopher Tolkien (ed.), The Silmarillion, "Akallabêth: The Downfall of Númenor"
- J.R.R. Tolkien, The Lord of the Rings, Appendix A, "The Númenorean Kings", "Númenor"
- J.R.R. Tolkien, The Lord of the Rings, Appendix F, "On Translation"
- Jason Fisher, "Sourcing Tolkien’s “Circles of the World”: Speculations on the Heimskringla, the Latin Vulgate Bible, and the Hereford Mappa Mundi" in Middle-earth and Beyond: Essays on the World of J. R. R. Tolkien, Kathleen Dubs and Janka Kaščáková (editors), Cambridge Scholars Publishing, 2010
|Constellations||Anarríma · Durin's Crown · Menelmacar · Remmirath · Soronúmë · Telumendil · Valacirca · Wilwarin|
|Stars||Alcarinquë · Borgil · Carnil · Elemmírë · Helluin · Luinil · Lumbar · Morwinyon · Nénar · Star of Eärendil · Til|
|The Airs||Aiwenórë · Fanyamar · Ilmen · Menel · Vaiya · Veil of Arda · Vista|
|Narsilion||Arien · Moon (Isil, Ithil, Rána) · Sun (Anar, Anor, Vása) · Tilion|
|See also||Abyss · Arda · Circles of the World · Eä · Timeless Halls · Two Lamps · Two Trees · Void|