Most Bible scholars assume that the ark was destroyed at the time of the destruction of Jerusalem by the Babylonians under the leadership of Nebuchadnezzar. Two other views are often heard. One is that Jeremiah hid the ark before the destruction of Jerusalem and that it just remains to be found or revealed when the Jews are ready to build the next Temple.
Another view is that the ark was supernaturally transported to heaven.
The major proof for this is Revelation 11:19 - "And the temple of God was opened in heaven, and there was seen in his temple the ark of his testament." The problem with the theory that Jeremiah (or someone else) hid the ark is that is is just a theory. No scripture or other reliable source supports this theory. As to the ark being transported to heaven: this is also nothing more than speculation. The fact that there is an ark in the heavenly temple does not mean it is the ark constructed by Moses.
There is a passage in Jeremiah that seems to disprove the alternative theories:
Jeremiah 3:16-17 And it shall come to pass, when ye be multiplied and increased in the land, in those days, saith the LORD, they shall say no more, The ark of the covenant of the LORD: neither shall it come to mind: neither shall they remember it; neither shall they visit it; neither shall that be done any more. At that time they shall call Jerusalem the throne of the LORD; and all the nations shall be gathered unto it, to the name of the LORD, to Jerusalem: neither shall they walk any more after the imagination of their evil heart.
First of all, this passage takes it as a given that the ark is still in Jerusalem during the time of Jeremiah. Second, it looks to a time when the ark of the covenant will neither be remembered nor visited. But this is not the time of desolation immediately after the destruction of Jerusalem. Rather, it is the time when the entire city of Jerusalem will be called the throne of god and all nations will come there to call on the name of the Lord. There is therefore no real need for the ark in the kingdom of God on earth. Why then would it be important to preserve it?
However, I will admit that even my belief that the ark was destroyed by the Babylonians has a certain bit of assumption. We are simply not given a direct statement as to its whereabouts. Perhaps it is not nearly as important as many think it is. I hope this helps.