Into the Woods and Fables: Are they Fairy Tales? What parts of the fairy tale tradition are kept?

The blog this week, which should still be written on the same schedule as always, and will be discussed on Friday, is a response to the viewing of Sondheim's Into the Woods and Willingham's Fables. How do these two interact with the fairy tale tradition? What do they keep? What do they leave out? What does this reflect about the times in which they were produced?