BIBLE HISTORY DAILY: Did Jesus Exist? Searching for Evidence Beyond the Bible. Lawrence Mykytiuk’s feature article from the January/February 2015 issue of BAR with voluminous endnotes. The answer to the question, of course, is yes, he did. Not that we necessarily know much about him beyond that. This article is a useful discussion, aimed at nonspecialists, of the earliest extra-biblical references to Jesus.
I was a little surprised not to see any reference to the published work of Ken Olson, who argues that Eusebius wrote the longer Testimonium Flavianum (a variant of Mykytiuk’s Alternative 2, which Mykytiuk rejects). More on that here.
Some past PaleoJudaica posts on the did-Jesus-exist question are, here, here, here, here, and here. I have touched on the question of the Historical Jesus occasionally. Some posts are collected in the last post linked-to in the preceding sentence, and see also here and (on the languages Jesus spoke) here and here.
More on Professor Mykytiuk's work is here and links.