Almost all of the tablets were identified as chronicles once in the collection of the British Museum, having been acquired via antiquities dealers from unknown excavations in the 19th century. All but three of the chronicles are unprovenanced.
The Chronicles provide the "master narrative" for large tracts of modern Babylonian history.
The chronicles are thought to have been written in Babylon during the Achaemenid period, c.550-400BCE. They are thought to have been transferred to the British Museum after 19th century excavations in Babylon, and subsequently left undeciphered in the archives for decades. The first chronicle to be published was BM 92502 (ABC1) in 1887 by Theophilus Pinches under the title "The Babylonian Chronicle". This was followed in 1923 by the publication of the Fall of Nineveh Chronicle (ABC 3), in 1924 by Sidney Smith's publication of the Esarhaddon Chronicle (ABC 14), the Akitu Chronicle (ABC 16) and the Nabonidus Chronicle (ABC 7), and in 1956 by Donald Wiseman's publication of four further tablets including the Nebuchadnezzar Chronicle (ABC 5).
The standard edition is A.K. Grayson, Assyrian and Babylonian Chronicles (= ABC; 1975)
A translation of Chronicle 25, discovered after the publication of ABC, was published by C.B.F. Walker "Babylonian Chronicle 25: A Chronicle of the Kassite and Isin Dynasties", in G. van Driel e.a. (eds.): Zikir Šumim: Assyriological Studies Presented to F.R. Kraus on the Occasion of His Seventieth Birthday (= Fs. Kraus; 1982).
John Brinkman revises Grayson's reading of ABC 1 in: "The Babylonian Chronicle revisited" in T. Abusch, J. Huehnergard, P. Steinkeller (eds.): Lingering over words. Studies in ancient Near Eastern literature in honor of William L. Moran (1990 Atlanta)
Fragments of the chronicles that are relevant to the study of the Bible, can be found in William W. Hallo (ed.), The Context of Scripture, volume 1 (2003 Leiden and Boston). This book also contains the Weidner Chronicle.
A recent update of ABC is Jean-Jacques Glassner, Mesopotamian Chronicles (2004, French version 1993)
An even more recent update of ABC is Amélie Kuhrt, The Persian Empire: A Corpus of Sources of the Achaemenid Period (Routledge, 2007)
The publication of I. Finkel & R. J. van der Spek, Babylonian Chronicles of the Hellenistic Period (= BCHP) has been announced.