ANSWER: The phrase "Ark of the Covenant" occurs at least forty-three times in the King James Bible. Not suprisingly, most of its occurences are found in the Old Testament.
Although one might expect the books of Numbers or Deuteronomy to use the phrase "ark of the covenant" the most, the writing that actually does so is authored by Joshua (Joshua 3:3, 6, 8, 11, 14, 17, 4:7, 9, 18, 6:6, 8 and 33). In the New Testament, this phrase used to refer to the ark given by God to the children of Israel is used only once (Hebrews 9:4).
There are, however, several other ways the Bible references the Ark of the Covenant. In the King James Version Bible this sacred object is also called the Ark of the Testimony (Exodus 30:6) and of the Lord (Joshua 4:11,1Samuel 4:6). It is also recorded as being called the Ark of God (1Samuel 3:3, 17, etc.), of the God of Israel (1Samuel 5:10), and of God's strength (2Chronicles 6:41).
The Ark itself was a very special container Moses built according to the specifications given to him directly by God (Exodus 25). It contained the stone tablets (given to Moses) which delineated the Ten Commandments (the basic terms of obedience from which the Old Covenant was built), the rod of Aaron the High Priest that budded, and a pot containing manna. Its first mention in the Bible is in Exodus 30.
The Ark was the holiest physical object located inside the holiest place in God's temple. It was in a special area commonly referred to as the 'Holy of Holies' or the 'Most Holy Place' and represented the throne of God. The room where this object resided was so holy that only the temple's High Priest could enter it once a year. If anyone else tried to go into the room where this sacred object was located, or if the High Priest entered it on a day other than what was commanded, they would be killed by God (Leviticus 16:1 - 2).
The Ark, which contained the words of the Covenant between God and his people, was likely destroyed by the Babylonian army. It was likely burned when Nebuchadnezzar, king of Babylon, leveled Jerusalem (including the temple) in 586 B.C.
We find an interesting statement in Jeremiah which declares that the ark and all that is with it will NOT be important during the Millennium (Jeremiah 3:16). What will be important will be the New Covenant God will offer all humanity. The book of Hebrews, chapter 9, explains that the spiritual or holy relics found in Jerusalem's Temple were mere patterns or copies of spiritual realities in heaven (Hebrews 9:1 - 5, 23 - 24).
Amazingly, Revelation 11 states that the Ark of the Covenant will be seen again in the near future. It will appear in the third heaven, the place where God's throne resides, after an angel loudly declares that the Lord is coming back to earth to rule all humanity (Revelation 11:15, 19)! This ark is not the physical object once found in the temple and transported to heaven but rather is the original composed of spirit essence.