Gospel Authorship: John

The Gospel of John is complicated, as it seems to have more than one author. The most obvious illustration of this is the final chapter, which is clearly a later addition. Though it is possible it is a later addition by the same author, I would have expected such an author to have felt free to change the previous chapter to make it fit; another author is likely to have considered the extant writing to be sacrosanct. See also John 21:24, which further indicates the author of this chapter was not written by the principle author:

John 21:24 This is the disciple who testifies to these things and who wrote them down. We know that his testimony is true.

It is quite dissimilar to the other gospels, being more spiritual in its approach, but also in the story it relates. For example, John has Jesus' ministry lasting for two to three years (three pass-overs), compared to only one in the synoptic gospels. John has Jesus crucified on the day of the passover (i.e., the passover was that evening, which would be the next day in the Jewish reckoning). In the synoptic gospels, the last super is the passover meal (the Seder). it has been said (by Jewish scholar, Hyam Maccoby) that the Jesus of John was more Greek than Jewish.

John

Most of the debate revolves around who the "beloved disciple" was. The gospel mentions him (or her?) several times, and indicates he is the author in some readings, leading many to speculate that it is the disciple John.

However, this exchange, from Mark 10, suggests that James and John were martyred, presumably before Mark was written (in fact, James is believed to have been martyred in 44 AD), making it very unlikely John was around to write a gospel.

35 Then James and John, the sons of Zebedee, came to him. ‘Teacher,’ they said, ‘we want you to do for us whatever we ask.’
36 ‘What do you want me to do for you?’ he asked.
37 They replied, ‘Let one of us sit at your right and the other at your left in your glory.’
38 ‘You don’t know what you are asking,’ Jesus said. ‘Can you drink the cup I drink or be baptised with the baptism I am baptised with?’
39 ‘We can,’ they answered.
Jesus said to them, ‘You will drink the cup I drink and be baptised with the baptism I am baptised with, 40 but to sit at my right or left is not for me to grant. These places belong to those for whom they have been prepared.’

This is further supported by references by some early church fathers. For example, Eusebius has this to say:

Moreover, Papias himself, in the introduction to his books, makes it manifest that he was not himself a hearer and eye-witness of the holy apostles; but he tells us that he received the truths of our religion from those who were acquainted with them in the following words.

But I shall not be unwilling to put down, along with my interpretations, whatsoever instructions I received with care at any time from the elders, and stored up with care in my memory, assuring you at the same time of their truth. For I did not, like the multitude, take pleasure in those who spoke much, but in those who taught the truth; nor in those who related strange commandments, but in those who rehearsed the commandments given by the Lord to faith, and proceeding from truth itself. If, then, any one who had attended on the elders came, I asked minutely after their sayings,--what Andrew or Peter said, or what was said by Philip, or by Thomas, or by James, or by John, or by Matthew, or by any other of the Lord's disciples: which things Aristion and the presbyter John, the disciples of the Lord, say. For I imagined that what was to be got from books was not so profitable to me as what came from the living and abiding voice.

What is significant here is that there are two Johns, the apostle and the presbyter. Papias never met the apostle, but was ever eager to learn more about him. It would seem likely that the reason they never met is that John was already dead. This view is contested; however, Papias has also been quoted as saying that John was martyred.

Furthermore, the Gospel of John does mention John the apostle in John 21:2, rather than referring to him as the beloved disciple (though this can be explained by invoking multiple authors).

Lazarus

A case has been made for Lazarus as the author. This is based, in part, on identifying the beloved disciple with Lazarus:

John 11:1 Now a man named Lazarus was ill. He was from Bethany, the village of Mary and her sister Martha. 2 (This Mary, whose brother Lazarus now lay ill, was the same one who poured perfume on the Lord and wiped his feet with her hair.) 3 So the sisters sent word to Jesus, ‘Lord, the one you love is ill.’

It should also be noted that John concentrates on events in Jerusalem much more than those in Galilee, which fits with a citizen of Jerusalem, like Lazarus, rather than a Galilean like John - but of course, there are plenty more citizens of Jerusalem that it could be.

John Mark

A case has been made for John Mark as the author, based in part on the Early Church Fathers believing the author was a John. I find the case weak, and the idea that this guy wrote two gospels seems unlikely, especially when we consider how dissimilar they are.

More here (it is free to download, but there are a lot of hoops to jump through):
http://www.academia.edu/1536543/John_Mark_-_Author_of_the_Gospel_of_John_with_Jesus_mother

No Beloved Disciple?

Perhaps though the beloved disciple was a literary invention. Compare Luke:

Luke 24:12 Peter, however, got up and ran to the tomb. Bending over, he saw the strips of linen lying by themselves, and he went away, wondering to himself what had happened.

With John:

John 20:3 So Peter and the other disciple started for the tomb. 4 Both were running, but the other disciple outran Peter and reached the tomb first. 5 He bent over and looked in at the strips of linen lying there but did not go in.

It would seem that a good case can be made that the author of John simply made up this beloved disciple, and inserted him into the narrative.

Not Even A Witness?

This verse, referring to the crucifixion, suggests the author was not himself a witness, but only recording the testimony of a witness:

John 19:35 The man who saw it has given testimony, and his testimony is true. He knows that he tells the truth, and he testifies so that you also may believe.

Dating

Around 90 AD, Jews started to exclude Christians from their synogogues. The Gospel of John alludes to this, but assumes it happened in Jesus' lifetime:

John 9:22 His parents said this because they were afraid of the Jewish leaders, who already had decided that anyone who acknowledged that Jesus was the Messiah would be put out of the synagogue.

John 12:42 Yet at the same time many even among the leaders believed in him. But because of the Pharisees they would not openly acknowledge their faith for fear they would be put out of the synagogue;

John 16:2 They will put you out of the synagogue; in fact, the time is coming when anyone who kills you will think they are offering a service to God.

This suggests the gospel was written some time after that (but there is good evidence it was before 140 AD), though it is possible these these were added by a later author.

That the author was confused on when this happened further argues against him being an eye witness himself.

I find it interesting that chapter 21, so clearly a later addition, seems to refer to the very earliest resurrection appearance; Jesus appearing to the disciples in Galilee as alluded to in the original Mark.

Summary

The consensus appears to be that the Gospel of John was written in Ephesus between 90 and 140 AD (probably nearer to 90 AD) by an anonymous Jewish Christian, and later went though at least two redactions.

More here:
http://www.huffingtonpost.com/john-shelby-spong/gospel-of-john-what-everyone-knows-about-the-fourth-gospel_b_3422026.html
www.webtheology.com/books/Identity_of_Papias_Elder_John.pdf
http://www.rejectionofpascalswager.net/john.html?
http://www.earlychristianwritings.com/john.html

Addendum, 03/Jun/20

An excellent review of the dating situation can be found here. The conclusion:

... None of the arguments for a pre-A.D. 70 date are strong arguments. However, evidence from John 20:28, the church fathers, Peter's death, and John 6:1 has proven decidedly more convincing. Based upon this, a date after A.D. 70 is more acceptable. The fact that the destruction of the temple was not mentioned, which leads one to think that a certain amount of time has lapsed, and the FG's relationship to First John, have led us to conclude that the FG was written between A.D. 80-100, with the most likely time being toward the earlier side of that range. Hendriksen tries to narrow down the date from A.D. 80-98, but is admittedly unable to do SO. One should not push the evidence further than it can go.