The first collected edition of Anglo-Saxon charters was compiled by John Mitchell Kemble, whose Codex Diplomaticus was published in six volumes between 1839 and 1848. Kemble's edition covers the whole of the Anglo-Saxon period, to 1066; but he was dependent to some extent on the services of a team of hired copyists, and it cannot be said that his texts are sufficient for modern purposes. Kemble's lead was followed by Walter de Gray Birch, whose Cartularium Saxonicum was published in three volumes between 1885 and 1893. Birch's edition provides a fundamentally reliable and accessible coverage of the period to the death of King Edgar, in 975; but for texts of charters issued in the period from 975 to 1066, we are still dependent on Kemble, and on other editions of charters that he missed.
The British Academy - Royal Historical Society edition provides texts of the entire corpus of documents, edited in accordance with modern standards. It differs from the editions produced by Kemble and Birch in two important respects. In the first place, the charters are edited not in chronological order, but on an 'archival' basis. That is to say, each volume contains the texts of charters formerly preserved among the muniments of a particular religious house, in order that the texts may be established and judged in relation to each other, and in relation to the recorded endowment of the religious house in question. Secondly, the separate volumes are provided with an introduction covering the history of the particular house and its muniments, with a detailed commentary on each charter, and a full apparatus of indexes.
[SDK - Kemble's Codex Diplomaticus, Birch's Cartularium Saxonicum, Crawford Charters, Chadwick's vernacular charters, and the BA/RHS edition. Links to CUP reprints.]