Who wrote the Book of Revelation?

We know that John the Apostle knew Jesus personally and intimately as cousin and close friend, so when John writes that he saw somebody that looked like "The Son Of Man" in Revelation 1:9. John is telling us that he knew what Jesus looked like. So by this clue we can infer that the person who wrote the Revelation is non other than John the Apostle!

Of course Revelation's author calls himself John, but your question is (at least largely) about the early external evidence on the identity of this John. The many references to the Apocalypse of John (e.g., in the title of one of Melito's writings, and throughout the manuscript tradition) don't speak to that (at least not directly). Let's survey the earliest pertinent evidence.

The lost writings of Papias (ca. 100) probably attested Revelation's authorship, although we know of it only indirectly. Andrew of Caesarea cites Papias among the authorities affirming its authorship by John the Evangelist (and, providing an otherwise-unknown quotation from Papias's work, has considerable credibility), though somewhat allusively. The fact that Papias was, according to Irenaeus, a "hearer of John" (in context, this John) would then imply essentially first-hand knowledge. Needless to say, practically everything about Papias is controversial to some extent.

Justin, Dial. 81.4 (ca. 155), writes: "there was a certain man with us, whose name was John, one of the apostles of Christ, who prophesied, by a revelation that was made to him...." The reference to Revelation is pretty clear, and Justin calls him one of the apostles. However, this need not necessarily mean one of the Twelve Apostles, as second-century writers also name Paul, Barnabas, and Luke as "the apostle", for example.

Irenaeus (ca. 185) has a lot to say about Revelation and repeatedly refers to its author, but his clearest statement is in Haer. 4.20.11: "John also, the Lord’s disciple, when beholding the sacerdotal and glorious advent of His kingdom, says in the Apocalypse," and after quoting from Rev 1 continues, "But when John could not endure the sight (for he says, 'I fell at his feet as dead;' [Rev 1:17] that what was written might come to pass: 'No man sees God, and shall live'), and the Word reviving him, and reminding him that it was He upon whose bosom he had leaned at supper, when he put the question as to who should betray Him [John 21:20], declared: 'I am the first and the last....'" So, Irenaeus unambiguously identifies John the Revelator with John the Evangelist (whom he elsewhere, like Justin, calls an apostle).

Among the Fathers, the first explicit identification of John the Revelator with John the son of Zebedee (and not simply as "John the Apostle"), is in Origen, Comm. Jo. 1.14 (ca. 230): "John, son of Zebedee, says in his Apocalypse...." This of course is entangled with the question of identifying the Evangelist with the son of Zebedee; Bauckham discerns such an identification already in two early apocrypha, the Acts of John and the Epistle of the Apostles, perhaps of the second century (though the dates are far from certain); on the other hand, Papias's mention of the martyrdom of the brothers James and John is usually understood as contradicting that identification. It continues to be debated today.

What about the denial of authorship by John the Evangelist?

Pseudo-Hippolytus's lost Chapters against Gaius (ca. 250?), a fictional dialogue between the orthodox "Hippolytus" and the heretic "Gaius", has the latter assert that Revelation (as well as John's Gospel!) was actually written by the heretic Cerinthus (famously opposed by John the Evangelist, as we read in Irenaeus). But this probably springs from misreading another fictional dialogue, the Dialogue with Proclus (probably by the real Hippolytus), where Cerinthus's apocalyptic forgeries and chiliastic views are briefly mentioned by the protagonist "Gaius". Anyway, Dionysius of Alexandria (ca. 255, in a lost work quoted in Eusebius) briefly mentions the allegation of Revelation's authorship by Cerinthus and dismisses it outright, but he goes on to question whether John the Revelator was indeed John the Evangelist, versus some other John, based on a comparison of style and content. Eusebius himself (ca. 315) notes the various prior positions affirming or doubting authorship by the Evangelist (assumed to be also the Apostle), and he speculates that the "John the Elder" cited by Papias was not the Evangelist (as Irenaeus says) but perhaps a distinct John who also wrote Revelation.

The above are the earliest evidence for the various ancient views on record. Although you also asked about scholars of the modern age, others more knowledgeable than I am will have to answer that.

I thought I should provide this information. I just want to point out that this is from an Eastern Tradition Perspective.

In Aramaic Revelation (From Crawford Codex manuscript) used in Some Eastern Traditions, you will see this title - "The Revelation which came to John the Evangelist from God in Patmos Island to which he was exiled by Nero Caesar." (Translation from Dave Bauscher's The Original Aramaic New Testament in Plain English, Pg. 363).

So it is believed among Aramaic Christians that Revelation is written by Apostle John during the time of Nero Caesar.

I found this by William Barclay in his Daily Study Bible in 17 volumes. This section is from Revelation of John Vol 1; the 1976 United States reprint.

http://www.dannychesnut.com/Bible/Barclay/Revelation,%20Part%20I.htm

THE AUTHOR OF THE REVELATION

(i) The Revelation was written by a man called John. He begins by saying that God sent the visions he is going to relate to his servant John (Rev. 1:1). He begins the body of his book by saying that it is from John to the Seven Churches in Asia (Rev. 1:4). He speaks of himself as John the brother and companion in tribulation of those to whom he writes (Rev. 1:9). "I John," he says, "am he who heard and saw these things" (Rev. 22:8).

(ii) This John was a Christian who lived in Asia in the same sphere as the Christians of the Seven Churches. He calls himself the brother of those to whom he writes; and he says he too shares in the tribulations through which they are passing (Rev. 1:9).

(iii) He was most probably a Jew of Palestine who had come to Asia Minor late in life. We can deduce that from the kind of Greek he writes. It is vivid, powerful, and pictorial; but from the point of view of grammar it is easily the worst Greek in the New Testament. He makes mistakes which no schoolboy who knew Greek could make. Greek is certainly not his native language; and it is often clear that he is writing in Greek and thinking in Hebrew. He is steeped in the Old Testament. He quotes it or alludes to it 245 times. These quotations come from about twenty Old Testament books; his favourites are Isaiah, Daniel, Ezekiel, Psalms, Exodus, Jeremiah, Zechariah. Not only does he know the Old Testament intimately; he is also familiar with the apocalyptic books written between the Testaments.

(iv) His claim for himself is that he is a prophet, and it is on that fact that he rests his right to speak. The command of the Risen Christ to him is that he must prophesy (Rev. 10:11). It is through the spirit of prophecy that Jesus gives his witness to the Church (Rev. 19:10). God is the God of the holy prophets and sends his angel to show his servants what is going to happen in the world (Rev. 22:6). The angel speaks to him of his brothers the prophets (Rev. 22:9). His book is characteristically prophecy or the words of prophecy (Rev. 22:7,10; Rev. 22:18-19).

It is here that John's authority lies. He does not call himself an apostle, as Paul does when he wishes to underline his right to speak. He has no "official" or administrative position in the Church; he is a prophet. He writes what he sees; and since what he sees comes from God, his word is faithful and true (Rev. 1:11,19).

When John was writing, the prophets had a very special place in the Church. He was writing, as we shall see, about A.D. 90. By that time the Church had two kinds of ministry. There was the local ministry; those engaged in it were settled permanently in one congregation, the elders, the deacons and the teachers. And there was the itinerant ministry of those whose sphere of labour was not confined to any one congregation. In it were the apostles, whose writ ran throughout the whole Church; and there were the prophets, who were wandering preachers. The prophets were greatly respected; to question the words of a true prophet was to sin against the Holy Spirit, the Didache says (Rev. 11:7). The accepted order of service for the celebration of the Eucharist is laid down in the Didache, but at the end comes the sentence: "But allow the prophets to hold the Eucharist as they will" (Rev. 10:7). The prophets were regarded as uniquely the men of God, and John was a prophet.

(v) It is not likely that he was an apostle. Otherwise he would hardly have so stressed the fact that he was a prophet. Further, he speaks of the apostles as if he was looking back on them as the great foundations of the Church. He speaks of the twelve foundations of the wall of the Holy City and then says, "and on them were the twelve names of the twelve apostles of the Lamb" (Rev. 21:14). He would scarcely have spoken of the apostles like that if he himself was one of them.

This conclusion is rendered even more likely by the title of the book. In the King James and English Revised Versions it is called The Revelation of St. John the Divine. In the Revised Standard Version and in Moffatt's and in J. B. Phillips' translations the Divine is omitted, because it is absent from the majority of the oldest Greek manuscripts; but it does go very far back. The Greek is theologos (GSN2312') and the word is here used in the sense in which we speak of "the Puritan divines" and means, not John the saintly but John the theologian; and the very addition of that title seems to distinguish this John from the John who was the apostle.

As long ago as A.D. 250 Dionysius, the great scholar who was head of the Christian school at Alexandria, saw that it was well nigh impossible that the same man could have written the Revelation and the Fourth Gospel, if for no other reason than that the Greek is so different. The Greek of the Fourth Gospel is simple but correct; the Greek of the Revelation is rugged and vivid, but notoriously incorrect. Further, the writer of the Fourth Gospel studiously avoids any mention of his own name; the John of the Revelation repeatedly mentions it. Still further, the ideas of the two books are different. The great ideas of the Fourth Gospel, light, life, truth and grace, do not dominate the Revelation. At the same time there are enough resemblances in thought and language to make it clear that both books come from the same centre and from the same world of thought.