The Ark was the symbol of the Covenant between God and His people.
What was it?
Exodus 25:10-22 "And they shall make an ark of shittim wood: two cubits and a half shall be the length thereof, and a cubit and a half the breadth thereof, and a cubit and a half the height thereof. And thou shalt overlay it with pure gold, within and without shalt thou overlay it, and shalt make upon it a crown of gold round about. And thou shalt cast four rings of gold for it, and put them in the four corners thereof; and two rings shall be in the one side of it, and two rings in the other side of it. And thou shalt make staves of shittim wood, and overlay them with gold. And thou shalt put the staves into the rings by the sides of the ark, that the ark may be borne with them. The staves shall be in the rings of the ark: they shall not be taken from it. And thou shalt put into the ark the testimony which I shall give thee. And thou shalt make a mercy seat of pure gold: two cubits and a half shall be the length thereof, and a cubit and a half the breadth thereof. And thou shalt make two cherubims of gold, of beaten work shalt thou make them, in the two ends of the mercy seat. And make one cherub on the one end, and the other cherub on the other end: even of the mercy seat shall ye make the cherubims on the two ends thereof. And the cherubims shall stretch forth their wings on high, covering the mercy seat with their wings, and their faces shall look one to another; toward the mercy seat shall the faces of the cherubims be. And thou shalt put the mercy seat above upon the ark; and in the ark thou shalt put the testimony that I shall give thee. And there I will meet with thee, and I will commune with thee from above the mercy seat, from between the two cherubims which are upon the ark of the testimony, of all things which I will give thee in commandment unto the children of Israel."
Deuteronomy 31:24-26 "And it came to pass, when Moses had made an end of writing the words of this law in a book, until they were finished, That Moses commanded the Levites, which bare the ark of the covenant of the LORD, saying, Take this book of the law, and put it in the side of the ark of the covenant of the LORD your God, that it may be there for a witness against thee."
2 Chronicles 5:10 "There was nothing in the ark save the two tables which Moses put therein at Horeb, when the LORD made a covenant with the children of Israel, when they came out of Egypt."
Where is it now?
There is a detailed account given of the items taken to Babylon from the "king's house" and the "house of the Lord" in 2 Kings 24:13, 2 Kings 25:13-18, and Jeremiah 52:17-23 but the Ark is not mentioned. Nor is it mentioned in the lists of things brought back from Babylon in Ezra 1:7-1:11. Clearly the ark was never removed.
But an answer to the location of the ark can be found in the following,
2 Baruch 6:1-10 "And it came to pass on the morrow that, lo! the army of the Chaldees surrounded the city, and at the time of the evening, I, Baruch, left the people, and I went forth and stood by the oak. And I was grieving over Zion, and lamenting over the captivity which had come upon the people. And lo! suddenly a strong spirit raised me, and bore me aloft over the wall of Jerusalem. And I beheld, and lo! four angels standing at the four corners of the city, each of them holding a torch of fire in his hands. And another angel began to descend from heaven. and said unto them: 'Hold your lamps, and do not light them till I tell you. For I am first sent to speak a word to the earth, and to place in it what the Lord the Most High has commanded me.' And I saw him descend into the Holy of Holies, and take from there the veil, and holy ark, and the mercy-seat, and the two tables, and the holy raiment of the priests, and the altar of incense, and the forty-eight precious stones, wherewith the priest was adorned and all the holy vessels of the tabernacle. And he spoke to the earth with a loud voice: 'Earth, earth, earth, hear the word of the mighty God, And receive what I commit to you, And guard them until the last times, So that, when you are ordered, you may restore them, So that strangers may not get possession of them. For the time comes when Jerusalem also will be delivered for a time, Until it is said, that it is again restored for ever.' And the earth opened its mouth and swallowed them up."
The Second Book of the Maccabees 2:4-8 "It was also contained in the same writing, that the prophet, being warned of God, commanded the tabernacle and the ark to go with him, as he went forth into the mountain, where Moses climbed up, and saw the heritage of God. And when Jeremy came thither, he found an hollow cave, wherein he laid the tabernacle, and the ark, and the altar of incense, and so stopped the door. And some of those that followed him came to mark the way, but they could not find it. Which when Jeremy perceived, he blamed them, saying, As for that place, it shall be unknown until the time that God gather his people again together, and receive them unto mercy. Then shall the Lord shew them these things, and the glory of the Lord shall appear, and the cloud also, as it was shewed under Moses, and as when Solomon desired that the place might be honourably sanctified."
The Israeli government admits that they know of a cavern beneath the temple mount, and how to access it, but refuse to for fear of an Arab uprising should they do so. There can be no doubt that the items are indeed below the temple mount.
Will it be seen again?
The next time mankind will see it will be on judgement day.
Revelation 11:18-19 "And the nations were angry, and thy wrath is come, and the time of the dead, that they should be judged, and that thou shouldest give reward unto thy servants the prophets, and to the saints, and them that fear thy name, small and great; and shouldest destroy them which destroy the earth. And the temple of God was opened in heaven, and there was seen in his temple the ark of his testament: and there were lightnings, and voices, and thunderings, and an earthquake, and great hail."