^Based on the way you worded that, I can't tell how much you already do or don't know about Gilliam, so at the risk of over-explaining:
Gilliam was one of the members of Monty Python, and went on to have a notable career as a filmmaker, with a really strange, distinct auteur style to his work. His film work is often weird, dark, fantastical, sometimes absurdist. And he's also known for his illustrations/animations, which have a similarly bizarre, distinct visual flair to them. All this to say that Terry Gilliam is an iconic (though divisive) artist, and Into the Woods seems like a really good fit for him. Not to mention he has rarely directed for the stage.
Again, apologies if I'm telling you stuff you already know, but hopefully I also answered your question in the process.