The Testimonium Flavian, or Testimonium Flavianum, is a passage allegedly written by Flavius Josephus which is often used by Christians to support a historical Jesus. It appears in section 18.3.3 of Josephus' work Antiquities Of The Jews, and scholars disagree on whether the passage is genuine to Josephus or whether it is a late interpolation by a Christian redactor.
The passage as we have it reads:
"Now there was about this time Jesus, a wise man, if it be lawful to call him a man; for he was a doer of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Gentiles. He was [the] Christ. And when Pilate, at the suggestion of the principal men amongst us, had condemned him to the cross, those that loved him at the first did not forsake him; for he appeared to them alive again the third day; as the divine prophets had foretold these and ten thousand other wonderful things concerning him. And the tribe of Christians, so named from him, are not extinct at this day."
There are three viewpoints taken by scholars on the passage:
- The passage, in its entirety, is genuine
- The passage is partly authentic but there have been Christian redactions
- The passage is a complete fabrication, possibly made by the fourth century Christian apologist Eusebius
Very few scholars take the first option. Passages such as "He was The Christ" would imply that Josephus was a Christian, when in fact he was Jewish.
There are, however, many defenders of the view that the passage is partly authentic. People who support partial authenticity restructure the passage to get rid of some of the more Christian elements, and come up with:
- "Now there was about this time Jesus, a wise man, for he was a doer of wonderful works. He drew over to him both many of the Jews and many of the Gentiles. And when Pilate, at the suggestion of the principal men amongst us, had condemned him to the cross, those that loved him at the first did not forsake him. And the tribe of Christians, so named from him, are not extinct at this day."
Arguments for authenticity
The typically Josephean language
Many of the phrases that are used in the Testimonium are typically Josephean.
Present in all manuscripts
The Testimonium is present in all manuscripts that we have. However, this is not a strong argument for authenticity because the earliest manucripts we have do not date earlier than the ninth century, and for the Greek manuscripts, the earlist date is the 10th century. 
Silence on the passage by church fathers
The passage is not quoted anywhere until we get to the fourth century. Origen, for example, never quotes it, despite the fact he wrote Contra Celsus in much detail, and relies on Josephus in other places in his work.
"To give one specific example. In Book I, chapters 46, 67 and 68 of Contra Celsum, Origen reports that Celsus had disparaged the miracles of Jesus, accusing Jesus of having learned his wonder-working tricks from the Egyptians. Origen counters this by claiming that Jesus’ deeds were superior to anything contained in the Greek myths, and that Jesus performed his miracles in order to win people over to his commendable ethical teachings, something no Egyptian trickster could emulate. An appeal here to the declaration by Josephus, a respected Jewish historian, that Jesus had been a 'wise man' who performed 'wonderful works,' would have served to place Jesus and his miracles in the favorable light in which Origen is trying to cast them."
This is an important objection to the authenticity of the Testimonium, because a positive reference to Jesus is unlikely to be ignored. Early church fathers were very familiar with the works of Josephus and often quoted him. It's very strange indeed that not a single one mentions this quote until Eusebius does in the fourth century. Eusebius is considered by historians to be the most likely candidate for the creator of this passage and, indeed, he is well-known as believing that a little white lie was justified if it furthered the cause of Christianity.
The shortness of the passage
The passage is incredibly short for Josephus, and it is a short digression for a character Josephus thinks is a "wise man". The interpolation view explains this fact: scrolls in the ancient world were of limited size, and manuscripts were not written on more scrolls than the original, as this would have made the manuscript difficult for readers to consult.
The passage comes in the middle of a collection of stories about calamities that happened to the Jews. The crucifixion of Jesus would not have been considered a Jewish calamity.
The passage interrupts the normal flow of the text. When the passage is removed, the end of the paragraph before it and the beginning of the paragraph after it merge perfectly.
Josephus was an Orthodox Jew and remained one his entire life. He would have never said such glowing things about Jesus. Indeed, he never would have called him "Christ" and yet remained a Jew his whole life.
Although Josephus reports the miracles of a number of other "prophets", he never once mentions any of Jesus' miracles. Whenever he writes about other prophets he blames them for famines, disease, wars, etc. and even calls them "false prophets". He never does so with Jesus, even though he should've thought such things seeing as he was a Jew.
The last line of the passage, "...subsists to this time", implies that the passage was written a long time after the events in question. Josephus himself, who lived so close to the time of Jesus, would never have written such a thing.
Josephus was neither a contemporary nor an eyewitness, but was reporting information received from others. The actual Testimonium Flavianum appears in Antiquities of the Jews which was published c. 94 CE, 60 years after the purported death of Jesus. On the other hand, many historical figures have no primary sources that report them.
The 20.9.1 Reference
Another quote from Josephus that's used by Christians is the following mention of James the Just:
"Festus was now dead, and Albinus was but upon the road; so he [Ananus, the Jewish high priest] assembled the sanhedrin of judges, and brought before them the brother of Jesus, who was called Christ, whose name was James, and some others, [or, some of his companions]; and when he had formed an accusation against them as breakers of the law, he delivered them to be stoned: but as for those who seemed the most equitable of the citizens, and such as were the most uneasy at the breach of the laws, they disliked what was done; they also sent to the king [Agrippa], desiring him to send to Ananus that he should act so no more, for that what he had already done was not to be justified; nay, some of them went also to meet Albinus, as he was upon his journey from Alexandria, and informed him that it was not lawful for Ananus to assemble a sanhedrin without his consent. (24) Whereupon Albinus complied with what they said, and wrote in anger to Ananus, and threatened that he would bring him to punishment for what he had done; on which king Agrippa took the high priesthood from him, when he had ruled but three months, and made Jesus, the son of Damneus, high priest."
- — Josephus, Antiquities Book 20: chapter 9
This quote isn't as obviously forged as the Testimonium, however there are good reasons to believe that it is or is at least an interpolation. Origen, Eusebius, and Jerome reference this passage, indicating it was present in their copy of Josephus but it still may be an earlier interpolation.
Out of place jargon
Josephus was writing for a Roman audience who would not have been familiar with Jewish beliefs concerning the Messiah. Indeed, they probably wouldn't even have known what the word "Christ" meant. To throw such a description in without any explanation would have confused the readers.
Why would Josephus suddenly mention Jesus before the person that the passage is actually about? On the other hand, if this were a Christian interpolation it would make sense to have Jesus' name be in the place of status, or the entire section may be about Jesus, but then in context it would be about another Jesus (son of Damneus) who in the end is made high priest.
After reading the rest of the text of this passage we find that the Jews were so angry about the stoning of James that they they demanded that King Agrippa fire Ananus. Why would the Jews be angered over the killing of a Christian, since Christians were seen as heathens by the Jews?
After the angry Jews get their way, "Jesus" is put in charge, Jesus son of Damneus and not Jesus son of Joseph. It seems as though "who was called Christ" was simply a margin note that got added to the text. The context would suggest that Jesus and James are brothers and after James is killed his brother is made to be high priest. And therefore the passage has nothing to say about any Christians but rather Jewish infighting.
The original Greek wording of the passage itself is extremely similar to Matthew 1:16 . For an Orthodox Jew this would be extremely unlikely.