I've been reading through an article in the most recent Journal of Biblical Studies entitled "The Yahwist: The Earliest Editor in the Pentateuch." Many of you know that just as there are theories about the sources of the Synoptic Gospels, there are theories of sources behind the Pentateuch.
100 years ago, Julius Welhausen's famous JEDP was being discussed and modified (and blasted). But of course the discussion has continued for 100 years, apparently with German scholarship still taking the most interest in such things. Welhausen's theory is not sacrosanct among scholars by any means--scholars can make their name by dismissing theories as well as suggesting new ones. A great deal has happened in discussion of this issue since him.
Mosaic authorship of the Pentateuch is still important in some circles for various reasons. Some pack more punch than others. Potentially the most powerful argument for Mosaic authorship is the way Jesus and the NT authors refer to it as "Moses says." But I'm not sure that this isn't simply "incarnated" speech, referring to the books in the way all the Jews of the day referred to the books. In any case the NT use of the OT is not a straightforward thing, since NT authors regularly read the OT "spiritually" rather than "historically."
This is the only significant argument for Mosaic authorship, since the books themselves don't "want" to be read that way. Genesis never mentions Moses and throughout the other four Moses is mentioned in the third person--we are told about Moses in them, including about his death. Nowhere is Moses said to be the author of the books themselves. From the standpoint of listening to these texts (rather than imposing ideas on them), we would not conclude that Moses put them in their current form. Of course sometimes faith requires belief in that which goes against the evidence.
In any case, the author of this article argues that someone he calls the "Yahwist" was the earliest editor of the material that is currently the Pentateuch. This author, he argues, spliced together six already existent stories, including those of Adam, Abraham and sons, Joseph, Moses, exodus, and Balaam. Later a priestly writer edited in further material, and Deuteronomy was added.
I have no stake in this debate and am not arguing for it. You might, however, find the web version of his "Yahwist" source interesting. The stuff in bold is what he thinks the Yahwist inherited and the italics is the Yahwist's editing, if I understand the site correctly.