Following on the first edition, Deuteronomy received three new editions, each separated from its predecessor by some forty years.
The second edition is known as the Torah edition, Torah meaning teaching, rule, law. Here Moses, the legendary founder of the nation, is portrayed in a post-Exilic context. Moses is its reputed author, and the text, 4:44 to 29:28, is presented as a ‘Torah’, that is, an instruction by Moses. The Torah edition highlights the special role of Moses in a prologue found in Deut 5, inserted between the rubric of the Covenant edition (Deut 4:45) and its opening section (Deut 6:4-9). The new prologue reminds readers how Yahweh made a covenant with the Israelites at Mt Horeb, and by means of the construct of an oral revelation, the scribe of this edition created room to insert new material into the law book he had inherited. The editor has supplemented the catalogue of curses appearing in Chapter 28 with a reference to the Judaean Diaspora: in case of disobedience, the Israelites will be dispersed among the nations. Karel Van Der Toorn concludes that this curse was made after the event, that is, it was coined on the basis of the Diaspora after the fall of Jerusalem in 568. Ergo, the editor lived in the exilic era, but when, since there is not a single allusion to a return from exile? Van Der Toorn concludes that the Torah edition comes from the beginning rather than the end of the Babylonian captivity and that the years between 590 and 570 are plausible.
The main contribution the Torah edition makes to the law code is the section on the various public offices, with the effect that what had been a law code became the constitution of a theocratic state. What had been a law code in the vein of earlier law codes became the constitution of a theocratic state run by the priests, who are superior to the king. The primary concern of the editor was to make sure that the monarch should be subservient to the priests.
In view of the symbolic role assigned to the King, the editor obviously did not live in the time of the monarchy. The ideal fits a time in which the head of state had little political power, such as the first decades of the Exile at the time of Jehoiachin. The scribe who wrote the Torah Edition was active in the first decades of the exile, as he was trying to come to terms with a venerated text strangely at odds with the realities of the time. Putting himself in the place of Moses, he supplemented the revelation of Moses with a vision of the future state of Israel where power was concentrated in the hands of the priests. The scribe who wrote such things did not describe a fact but an ideal, and probably came from the Levitical priests who were administrators, judges and scholars.
In the History Edition, the Covenant and Torah are interchangeable notions. From a reform document and later a theocratic vision, Deuteronomy became part of a historiographic project. Its scribe added chapters 1-5 at the beginning and chapters 27 and 31-34 at the end. More so than in the Torah edition, the focus is on Moses, framing events with references to the sins and apostasies that the Israelites would commit after the death of Moses. The scribes of the History edition, who come across as educated clerics, read the national history as a theodicy of the Exile.
The Wisdom Edition represents the last major redaction of Deuteronomy. The scribe who wrote it was less concerned with the notion of a covenant than with the intellectual significance of the Jewish way of life. Chapters 4 and 30, the focus of the Wisdom edition, provide a clue as to the time of the editor. Deut 30:1-5 contemplates the possibility of a conversion of Israel followed by a return of the exiles, then scattered all over the world (cf also Deut 4:29-30), which probably means that the editor lived in the time after the Exile, and that the Wisdom edition itself was written by a Babylonian Jew in the early Persian period. The Wisdom edition gives a new dimension to Deuteronomy, a dimension which consists in the self-confident affirmation of the superiority of the Jewish way of life. The editor condemns the worship of images, and emphasises that the laws are commensurate with the human intellect. Its editor was probably a teacher himself. He viewed the Jewish way of life as an enlightened way of life glowing with the wisdom of the Torah.
 This is an adapted summary of Scribal Culture and the Making of the Hebrew Bible. Karel Van Der Toorn, Harvard University Press, Cambridge, 2007, 150-172.