We can rely upon them for the major events, like the outcome of wars, the participants, the names, the characters, the reasons for wars, etc. But Thucydides and Livy were great at putting speeches in the mouths of generals - very good speeches, and worth reading, but questionable as an accurate account. They also are unreliable about the numbers of men in a battle or the numbers of casualties; we can't verify the numbers, but some of them seem inflated. Herodotus seems to have taken folklore as history on certain topics, like the hanging gardens of Babylon. Tacitus had a romantic view of German barbarians, and this kind of personal bias was not a consideration in ancient historians. Suetonius likewise wrote a biased account of the 12 Caesars, though this doesn't mean that what he said isn't true, just cherry picked. Unbiased history is modern.