The “J” source has its origins long before Wellhausen’s paradigmatic reformulation of pentatuechal source theory, but it was Wellhausen, along with Reuss and Graf that insisted that P, with its laws was the latest source, and insisted on J being set within the monarchic period. This seems to fit the general tenor of the European world at that point which tended to negatively evaluate priests and ritual as having muddled and confused earlier pristine beliefs. J, however, was always vaguely defined; it was the leftovers when the more easily identified layers (EDP) had been identified, and it was a continuous debate in the 20th century about where J ended. J is, of course, known for its use of the divine name “Yahweh” as well as its anthropomorphic depiction of God.
By 1970, a consensus about J and the great documentary hypothesis had been reached building off of the efforts of Gunkel, Noth, and von Rad. Gunkel has pioneered the use of form criticism to access the oral origins of the preexisting sources that J had at his disposal. Noth explored the sources that J had at his disposal and postulated a G source for both J and E. Von Rad saw important theological themes found in creeds within the Pentateuch that demonstrated the J writer’s theological intent, and theorized that such had occurred in a time of enlightenment during the Solomonic period.
This consensus was shattered subsequent to 1970 and a new consensus has yet to be formed. For example, Rendtorff opened up the discussion for the complete rejection of the documentary hypothesis and instead employed form criticism to analyze individual smaller units, focusing on the main themes of the Pentateuch, rather than sources. Van Seters radically reanalyzed the older consensus by arguing that the DH precedes JE and that JE provided an introduction to the Deuteronomistic material. Today scholars have adopted a range of opinions, with a large number of older scholars adopting a “wait and see” approach, holding to the shaken older paradigm since there is nothing yet to replace it.
ABD VI:1013-1020; Gordon J. Wenham, "Pondering the Pentateuch: The Search for a New Paradigm," in Arnold and Baker, The Face of Old Testament Studies: A Survey of Contemporary Approaches, p. 116-144