These SAW movies keep on getting better and better.
Although Jigsaw is dead, he's still very much a presence in this installment of the franchise. In fact, the movie starts off with his graphic autopsy, as they remove his brain and open his stomach. They find a cassette tape in his stomach and when the police detective plays Jigsaw says the games will continue.
The police suspect there is a third person who has been helping Jigsaw, though it's a bit more complicated than that. Through his manipulation, he's able to get a lot of his victims to torture and test themselves. There are lots of flashbacks, particularly of Jigsaw and his wife, which clarifies why he went insane. It wasn't just because he had cancer - it's something even worse.
The tortures are gruesome and the movie is fast moving. I liked the surrealistic transitions between a lot of the scenes. IV is the best SAW yet.