For the sake of comparison, let’s just put a few of the theories out there. I will select just the most common for the Torah/Pentateuch:
1. Wellhausen’s Documentary Hypothesis - that the Torah shows evidence of at least two and as many as five different textual layers, dating from pre-monarchy to post-exile.
2. Rosenberg’s “Royal Lady” - that the primary document of the Torah were written in the court of Solomon and/or Rehoboam.
3. Finkelstein’s Josiah Theory - the entire Torah and the histories were written to demonstrate Josiah’s kingdom’s legitimacy.
4. P. J. Wiseman’s Ancient Record Hypothesis - Moses, or a similar editor, compiled existing records and they remain largely as they were.
5. Traditional Conservative/Orthodox Judaism - Moses received the Law and wrote the Torah directly from God. There have been no alterations since then.
I understand that most of us do not follow one school of thought or the other and the concept of the emerging church is to deconstruct everything, but if you had to choose one you lean toward, which would it be?

Theories of composition
I’m as interested in the issues raised by theory of composition as the theories themselves. Theory of composition can become a fault-line between the tectonic plates of speculative, ‘critical’, ‘modernist’, ‘liberal’ interpretations of scripture and ‘conservative’ interpretations resting on a belief in their divine authority and inspiration. Somehow I think the two viewpoints need to engage with each other. (The discussion is also a welcome relief from the individual/corporate salvation teacup-storm raging elsewhere!)
Conservative scriptural expositors tend to want there to be single, divinely inspired authors of scriptural texts, the texts themselves being composed at the point in time to which they refer, with a leaning towards establishing a literal version of history ‘as it actually happened’. In this mind-set, a key battle-ground is taken to be that of proving the historical veracity of scripture as a foundation of faith, as opposed to those who are seen as discrediting faith on the grounds of historical unreliability.
Theories other than this rather caricatured conservative version do not necessarily undermine the foundational principles at issue: redactive layering in the texts does not exclude the divine Spirit’s superintendence of the texts themselves; theological interpretation and editing of history does not necessarily undermine the historicity of events. All history is interpretive and selective according to the viewpoint and interests of the historian.
Non-‘conservative’ theories of composition can be seen as a threat to assertions articulated in statements of faith - which commonly refer to the divine inspiration of the scriptures “as originally given”. The assumption is that the earliest versions of a document must be the most accurate and therefore authoritative. Since we do not possess the scriptures “as originally given” the assertion has always seemed to me to be rather less than useful. However, the possibility of original documents out of which potentially conflicting viewpoints were cobbled together in the scriptures (such as J,E, P, and D in the OT), makes “as originally given” doubly embarrassing to this particular conservative obsession.
Theory of composition can be used to reinforce political agendas. Instead of an ‘authoritative canon’, the scripture can be seen as something of a ragbag collection in which various parties are in dispute with each other. We have the Jahwist, Elohist, Priestly and Deuteronomist camps each vying for the supremacy of their own version (whatever that might be) of events. There are the diehard nationalists seeking to preserve the purity of the race, and those who take a more inclusive, open attitude to the rest of the world (Ezra/Nehemiah v. Ruth, Jonah). The warring camps idea then spills over into the NT: Matthew is said to reflect anti-semitic prejudice in the early church; Luke is more affirming of the Jews; Paul is said to have been a congregationalist with regard to church government; his pseudepigraphers in 1 & 2 Timothy had a more catholic, hierarchical version of church government. Paul and Mark are said to have advocated freedom from old covenant requirements and practices; James and Matthew sought to enforce them.
Perhaps the notion of theories of composition becomes more relevant to contemporary concerns when it is suggested that biblical documents are the product of a rather extended editorial process which involved community reflection on the events they describe. Instead of God speaking directly to the communities through divinely inspired authors, the communities themselves become part of the authoritative process. Some would say that the authority of the texts is invested entirely by the communities themselves; texts do not have an inherent authority. A very postmodern position.
Or maybe the divine Spirit works through a process of community reflection - which might not be so far from what happens in in all ages and today - where the community of God’s people reflects on the meaning of the texts for themselves in contemporary life. The fault-line here would be between those who seek to do so under conscious submission to God’s authority and guidance, and those who feel that the rational intellect can be the final arbiter. One might also want to include those who recognise that ‘meaning’ does bring into play the relationship between historical context and current understanding and application.
I’ve deviated a long way from the simple question at the head of this thread, so I’ll bring my own somewhat simplistic response to the introductory question: I take the view that there may well have been a certain amount of redactive layering taking place in the assembling and recording of scripture (since we have no definite evidence for this it must remain a subject of speculation). In the OT, Deuteronomy in particular towers over the experience of Israel throughout Judges, 1 & 2 Samuel, 1 & 2 Kings, the Prophets and the experience of Israel in the exilic and post-exilic period. The striking relevance of the ‘earlier’ parts of the OT to the period of exile and return almost seems to demand a view of editorial compilation (composition?) close to that period. Parts of Deuteronomy read like contemporary commentary on the exile. Nevertheless, my view is that Deuteronomy and the Pentateuch were essentially early - at least 1000 years before the exile; and especially that this was not ‘mythical’ history - in the sense of history being concocted as a ‘backwards projection’ in the light of contemporary pre- or immediately post-exilic experience.
I find the ordering of OT books in the Hebrew assembly of the scripures provides helpful insights - with the threefold division of Law, Prophets and Writings pointing to the theological significance and unity of the texts they contain. For what it’s worth, I think there is a good case to be made for single authorship of Isaiah (though this would be howled down with derision in most academic establishments) - but it’s not a crucial issue as far as ‘divine inspiration’ and ‘authority’ are concerned; I take all of Paul’s letters to be Pauline until better evidence is produced for pseudepigraphical authorship - but this need have no bearing on their ‘authority’. I find the supposed conflicts between Paul/Mark and James/Matthew to be spurious; and I would have no problem with a late authorship of Daniel - whose location in ‘the writings’, rather than ‘the prophets’ of the Hebrew scriptures might be significant.
These ramblings may be somewhat tangential to the topic of the thread, but I’d be interested to hear from those who have researched things more thoroughly than myself. The journey can be as interesting as the destination in these reflections.