Charity never faileth: but whether there be prophecies, they shall fail; whether there be tongues, they shall cease; whether there be knowledge, it shall vanish away. Much of the context of 1Cor, particularly chapters 12 and 14, concern spiritual gifts, among them being miraculous tongues speaking, knowledge and prophecying. So this verse is speaking of the gifts of these things. Thus, knowledge in general still exists, and prophecy does, in that prophecy is the giving of God's revealed will, which every godly preacher does when he preaches a scriptural sermon, and tongues, as far as human languages still exist. And as has been testified of here, and I have heard of the same thing occurring, the Lord still, from time to time, opens the ears of understanding of the lost to hear the gospel, even if spoken in a different language than they understand. But that's different than the gift spoken of in 1Cor 14. So clearly, due to context, we know that this verse is speaking of the miraculous gifts.
For we know in part, and we prophesy in part.
We know in part and prophecy in part-this means that as the Lord gives the gifts of knowledge and prophecy, it is partial-no one person was given ALL prophecy or ALL knowledge-each prophecy was for a reason, and was a part of the totality of prophecies the Lord would give for His people, be they Israel or the churches.
But when that which is perfect is come, then that which is in part shall be done away.
This verse juxtaposes the previous verse, speaking of 'in part', thus, perfect does, indeed, mean 'complete'. In part/perfect...in part/complete. That which is perfect refers to the completion of the word of God, what we call the canon of scripture. Once that was complete, Once the Lord gave the last prophecy, the last revelation of His will and word, that which was perfect came, and thus, that which was in part was done away.
Tongues, generally-speaking, were given for one primary purpose: as a sign to unbelieving Jews, as a fulfillment of prophecy. 1Cor 14:21 says "In the law it is written, With men of other tongues and other lips will I speak unto this people; and yet for all that will they not hear me, saith the Lord." This prophecy is found in !saiah 28:11 & 12: "For with stammering lips and another tongue will he speak to this people. To whom he said, This is the rest wherewith ye may cause the weary to rest; and this is the refreshing: yet they would not hear." Tongues was given for the sake of the Jews, as a sign that their promised rest in the Messiah had come, yet, in Isaiah, they were warned that they wouldn't hear it, and so it came to pass. These are those referred to in 1Cor 14:22, :"Wherefore tongues are for a sign, not to them that believe, but to them that believe not: but prophesying serveth not for them that believe not, but for them which believe." Once they rejected completely, once the canon of scripture was completed, tongues as a GIFT ceased. It doesn't mean, again, that the Lord can't use it as He did on Pentecost, which is, as I read it, the same way it was testified here, not so much necessarily a miracle of speech, but a miracle of understanding, though that could be argued. But when you hear that someone who understands NO English, yet understands the gospel in English, it seems to make sense.