Quite a bit - in fact, we have more evidence of Jesus' existence than of a lot of other figures from the time. We have more evidence of Jesus' existence than Gisgo the Carthaginian. (My favourite Carthaginian, it bears noting.) I commend to your attention the section of the FAQ that deals with the evidence of Jesus' existence.

Any miracle business that Jesus may or may not have done is, however, not within the bailiwick of history. All miracle-related inquiries are better made to the Theology Department, over in the other building.