There are many controversies regarding the art (or, according to some who don't like him, his "not art") and I must say I also have mixed feelings for his works. First of all, I simply don't like his pieces featuring dead and dissected animals and I think many times it's more about provoking scandal and common disgust and not about creating something that gives something spiritual, supernatural to people.
BUT. He has other works as well, of course, and even if they still have many things from his normally "morbid" point of view, I do think some of these pieces are great and very grotesque - these are the moments where he manages to find the balance between disgusting and attracting, these are something that make you want to turn your head away and stare for hours at the same time. And I think this is why his art can be called art, even if I totally agree with those who say "a dead shark is not art".
Adam and Eve under the table
The picture below is not completely Damien Hirst but I think the composition is great , maybe because I can't properly see if the Hirst piece is made of animal organs...? Anyway, the gorilla is brilliant.
Damien Hirst Butterfly wallpaper 2003 © the artist/Courtesy Jay Jopling, London
Damien Hirst The Pursuit of Oblivion 2004 (detail) © the artist/Courtesy Jay Jopling, London
Sarah Lucas Spam 2004 © the artist/Courtesy Sadie Coles HQ, London
Angus Fairhurst The Birth of Consistency 2004 © the artist/Courtesy Sadie Coles HQ, London
The last picture belongs to Tate Britain