Here are the passages about Josephus and the TF and Tacitus:
The infamous "Testimonium Flavium" appears to have been inserted into the Antiquities about the time of the 4th century. A key proof for this comes from the fact that while early Christians cited Josephus, none of them ever cited the Testimonium, even in situations where they were striving to provide historical proof for Jesus (i.e. in debates with Jewish scholars):
Justin Martyr (circa C.E. 100-165) never once quoted the passage -- even in the face of charges that Christians had "invented some sort of Christ for themselves" and that they had accepted "a futile rumor" (Dialogue with Trypho 8; circa C.E. 135).
Clement of Alexandria (ca. 192) - familiar with the works of Josephus
Tertullian (ca. 193) - familiar with the works of Josephus
Origen (circa C.E. 185-254), who in his own writings relies extensively upon the works of Josephus, does not mention this passage or any other passage in Josephus that mentions Christ. Not even when he is in dialogue against Celsus' accusations!
Jerome (circa C.E. 347-420) cites Josephus 90 times, but never once cites the Testimonium.
(citation: Lost and Hostile Gospels, Rev. Sabine Baring-Gould)
Logic itself tells us that had Josephus written the Testimonium, he would have written more than 3 lines concerning the existence of the Jewish Messiah in a book dedicated to Jewish History! You can't mention the Jewish messiah in passing in a book dedicated to a history of Judaism. You might as well write a book called "The Solar System" without mentioning the sun, except in a footnote on page 474.
Remsberg writes on this point poignantly:
"Its brevity disproves its authenticity. Josephus' work is voluminous and exhaustive. It comprises twenty books. Whole pages are devoted to petty robbers and obscure seditious leaders. Nearly fourty chapters are devoted to the life of a single king. Yet this remarkable being, the greatest product of his race, a being of whom the prophets foretold ten thousand wonderful things, a being greater than any earthly king, is dismissed with a dozen lines."[11]
It's brevity in fact points to interpolation:
Richard Carrier writes:
"An expert on manuscripts would know the problem here: scrolls have a fixed length. Each book of a work usually had to be no larger than would fit on one scroll, and certainly it was problematic for a copyist to break the pattern and use more scrolls than his source text (it would throw off everything, and make consulting the work a nightmare for any reader). This fact argues in favor of interpolation. If the material came from Josephus, he could have written more about such a topic (surely, since as we now have it, it is a marvelous digression indeed to warrant so slight a coverage), and just ended the whole book sooner, thus creating no problem. But if the material was added by a later editor, there would have been very little space to work with: so the addition had to be short, short enough to prevent the whole book from exceeding a standard scroll's length. (The interpolation was perhaps made by the 4th century Christian librarian Eusebius: see Kirby's "The Testimonium Flavianum."[12]
Logic also provides us with yet another powerful clue as to the falsity of the Testimonium: Josephus lived and died a Jew, never converting to Christianity. Why would he call Jesus "the Jewish Messiah" in the text? Even a Christian apologist, normally at home with warping logic well past its breaking point, ought to find it difficult to reconcile the claim that Josephus had any substantial evidence of Jesus as the Messiah with the fact that he never converted to Christianity. How could Josephus have good evidence for the existence of a messiah, and yet, at the same time, die a Jew?
There's really only one way to salvage the Testimonium: to use Jeffery J. Lowder's argument that the Testimonium was radically altered by Christians, and that the original Josephus passage was a second hand reference to a purely human Jesus who, while worthy of a brief note, did not merit more than a few lines of text, let alone consideration as the Jewish Messiah. This would explain why Christians did not cite it until it was radically altered: because it was an actual refutation of the gospel claim of Jesus the Christ.
Lowder writes:
"There are many scholars who believe the original text contained an authentic reference to Jesus but was later embellished by Christian copyists. I have italicized the sections widely regarded as interpolations":
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 among 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.
Lowder states that this may explain why no early Christian cited the Testimonium: because it did nothing to support the existence of Jesus as Jesus the Christ.[13]
The two most plausible explanations for the Testimonium: that it is either entirely or partially a fraud, both create a serious problem for the Christian.
If the Testimonium is a complete fiction, it leaves the christian without any historical corroboration from Josephus.
If it is a tampered document, it shows that there is a non contemporary account of Jesus, one who may even meet one of the criteria mentioned in Mark (drawing crowds). But it indicates that Josephus did not consider this Jesus to be anything more than a revered teacher - literally noteworthy - but hardly the wonder worker of the book of Mark, a fact that embarrassed early Christians to the point that they 1) ignored the passage for centuries, even while citing Josephus elsewhere and 2) later saw fit to deceptively alter the passage.
It should also be noted that some argue that Antiquities section 20.9 makes an indirect reference to Jesus. This claim is examined here:
http://www.inu.net/skeptic/gospels.html There is good reason to believe that the reference to a "Jesus' here is actually a reference to Jesus, son of d--neus that has been tampered with by later Christians, and not an actual reference to 'Jesus, son of Joseph', although Origen does cite this passage as historical evidence for Jesus. And again, the same point remains: the idea that a historian would mention the Messiah in passing while discussing an issue of minor relevance (and not elsewhere) staggers reason itself.
[edit] Tacitus
Tacitus (ca. 56