A fairly good short summary by Nick Backstrom in his blog, Things that I found. He leads up to this:
But even if you don’t believe in the Shroud as the burial cloth of Jesus, there are still questions that have to be answered. Why did other scientific testing, finding blood and other materials, tend to prove it authentic? Why did a Medieval artist choose to do an anatomically correct crucifixion when no-one, no-one, else depicted it that way? And finally, how was it done? Despite many efforts, no-one has been able to recreated a Shroud in any way that is believable or practical. Leonardo da Vinci has been mentioned of course, but the Shroud, even as a fake object, existed before he did. (One wonders how Leonardo found time to do anything with all the conspiracies he up to his hips in.) Even as a fake, the Shroud still poses questions for which we cannot find answers
Link: Things that I found: "That wraps it up!": The Shroud of Turin