Historicity of Jeremiah and his works

The consensus seems to be that there was a historical Jeremiah and that portions of the book probably were written by Jeremiah and/or his scribe Baruch. However it also went through several extensive redactions in the exilic and post-exilic periods which added material and altered the wording of oracles. This resulted in variant editions of the book (LXX, 4QJer, MT). Sometimes it is clear that the LXX reflects the earlier wording, such as in Jeremiah 25:8-12.

Here’s the extensive analysis in Rainer Albertz’ Israel in Exile (2003, SBL), pp. 302-344. First there were early collections of oracles, including material in ch. 2-6, 8-10, 13, 21-23, etc. Then there was an early Deuteronomistic redaction which Albertz dates to around 550 BC, with the original ending to the book at 25:13. There was a second redaction around 545-540 which added much more material, up to about ch. 45. Then there was a third redaction around 525-520 expanding the book up to the ending at 51:64. Then there were further post-exilic redactions adding ch. 52 and editing content throughout the book.
Although Jeremiah was often thought of traditionally as the author of Lamentations, this is probably a collection of individual and communal laments composed at various times throughout the exile. Albertz considers ch. 2 as the oldest, dating shortly after the destruction of Jerusalem and ch. 5 after the assassination of Gedeliah, with the other chapters added later (p. 160).