Pretty much everyone agrees that Acts was written by Luke who also wrote the Gospel of Luke. It is also agreed that Acts was written after Luke. The major proof of this is that they both start off addressed to the same guy, Theophilus, and Acts references a first book about the life of Jesus. Near the end of Acts (around chapter 18) the author writes themselves in with travelling around with Paul, and Paul seems to reference Luke three times in his letters. Also the earliest copies of Luke is ascribed to him, and people think that there is no good reason for the church to ascribed these works to a small figure like Luke, unless he was the guy who actually wrote them. And some people say that the writing styles are the same...
If the Gospel of Luke was written after 70 AD then the big question is: why did Luke not mention Jerusalem or the Temple been destroyed when he wrote Acts? It's not like Luke didn't talk about Jerusalem. The Gospel of Luke refers to Jerusalem the most out of the other Gospels (30 times), and Acts refers to Jerusalem the most out of any other New Testament writings (58 times). Jerusalem plays a key place in the book of Acts. It starts off set in Jerusalem, where the first Christian church started and then the Christians who were travelling all over the shop go back to Jerusalem to visit key people there (like Peter - the leader of the Apostles, James - the brother of Jesus and John - the beloved disciple), or plan going back there as it was the place where the first church had started. In Acts 15 there is even an important council that took place in Jerusalem. Paul also started raising money for the church in Jerusalem.
The destruction of Jerusalem would have been a big deal, and for Jewish people it would have probably been the biggest event that century for them, as their temple was destroyed. Back then it is good to remember that religion wasn't some private personal thing separated from politics; religion was ingrained in all parts of the Jewish culture. It seems strange that Luke doesn't record this war. He was after all trying to give an account on the early acts of the first Christians, and since Jerusalem was where it all started and where some key people were located, it would have been strange for him to just skip over it, that is if it was written after 70 AD. There isn't really a good reason as to why this is left out, unless it hadn't happened at the time of writing.
Overman quotes Gregory A Boyd:
For an author where narrative is centrally structured around Jerusalem (Luke 24:13; Acts 1:8) and who makes frequent mention of the temple (Acts 2:46; 3:1–2, 8, 10; 5:20–25; 21:28–30; etc.), their omission is most surprising. For an author who took the time to mention the much less significant expulsion of the Jews from Rome under Claudius (18:2), the omission is indeed astounding. And for an author who is interested in how persecution of the church helped spread the Gospel around the world (e.g., 8:4), this omission comes close to being inexplicable—except on the supposition that he had no knowledge of these events! (p90)Overman also quotes John A T Robinson on how none of the New Testament writings mention the destruction of the temple:
One of the oldest facts about the New Testament is that what on any showing would appear to be the single most datable and climactic event of the period—the fall of Jerusalem in A.D. 70, and with it the collapse of institutional Judaism based on the temple—is never once mentioned as a past fact. It is, of course, predicted; and these predictions are, in some cases at least, assumed to be written (or written up) after the event. But the silence is nevertheless as significant as the silence for Sherlock Holmes of the dog that did not bark. . . . Explanations for this silence have of course been attempted. Yet the simplest explanation of all, that ‘perhaps . . . there is extremely little in the New Testament later than A.D. 70’ and that its events are not mentioned because they had not yet occurred, seems to me to demand more attention than it has received in critical circles. (p90-91)