Before I begin, there will be spoilers. And do not watch this movie.
That said, it's a good movie. It's very well made. Lars Von Trier has painted a very accurate and disturbing portrayal of your typical, brighter than average serial killer.
In so doing he has created a very, very, evil film.
The plot - the adventures of a serial killer named "Jack" - well, as grim as it is to suggest it's enacted daily. But we know this, we don't need a movie about it. How many movies are there about Serial Killers - from the camp - "Silence of the Lambs" to "Henry, Portrait of a Serial Killer" or "Man Bites Dog" or "M" or any of a hundred other films, the genre, the subject has been thoroughly and well explored.
The filming - amoral, almost glamorizing or celebrating Jack's killings. Allowing Jack to speak to Vergil, to "explain" himself - is wrong. We don't need his explanations. No explanation, expatiation or narration can excuse this. And here is where I take issue - details of real serial killings are often scant for the good reason they don't care to inspire copycats. This movie will inspire copycats.
Do not watch this movie. It is very disturbing. It is very accurate. You will learn nothing. It is pornographic in it's savagery, in it's desire to offend and terrorize the audience more and more. You don't need this. You don't want to become jaded to this. The people that watch this movie, that enjoy it, they won't be the audience that applauds the references to "The Inferno", if they were they would slap Lars Von Trier silly over the ending (it should have ended some 30 seconds earlier, his final scene is a transparently cheap attempt to add some morality or justice to a movie that clearly has none).
DeSade - for all his filth and corruption, had an underlying morality, and wrote within his tastes to explore larger philosophical issues. This movie does not do this. Or perhaps it does, and in my initial offense I've overlooked it, but ----
Matt Damon acts very convincingly the role. I don't know how he did this without suffering some "collateral damage". To be in a movie that goes this deep into it's subject matter, well, it has to take it's toll.
This is an evil movie. There is no need for it. It's gratuitous, it's like watching ISIS beheading people, or footage of accidents in which no one survives, or videos of torture or a hundred other such violations, it revolts, it disturbs, it churns the stomach and imagination, and worst of all it gives an ironic voice to that class of criminal from whom no voice should be heard. There is no morality to it - perhaps that's it's greatness, but I would disagree.
This is an evil movie. Do not watch this. I've warned you.