The Big Names in Textual Criticism
So, we've already mentioned them—A. W. Pollard, R. B. McKerrow, and W. W. Greg were the big bad Brits who started it all. Pollard was one of the first guys to systematically study and classify Shakespeare's works in their various versions. His 1909 book Shakespeare Folios and Quartos: a Study in the Bibliography of Shakespeare's Plays, 1594–1685 is a milestone in the field.
McKerrow and Greg are known for different reasons, though they were both also big Shakespeare fans. McKerrow is the dude who gave us the first definition of the "copy-text." In 1914, he also wrote an important book called An Introduction to Bibliography for Literary Students, one of the first books to explain and clarify the core principles of Textual Criticism.
Greg followed in McKerrow's footsteps. He wrote a famous essay called "The Rationale of Copy-Text," in which he took up McKerrow's definition of the copy-text… and then basically disagreed with McKerrow's whole approach.
Greg's ideas on the copy-text became important for the generation of Textual Critics who came after him. Two names to keep in mind are Fredson Bowers and G. Thomas Tanselle. Bowers, in particular, developed and elaborated Greg's ideas, applying them to the editing and criticism of literary works.
Finally, Jerome McGann and John Bryant are a couple of rebels in the field: they took up positions that put them at odds with the big guns of Textual Criticism, people like Bowers, Tanselle and Greg. They started focusing more on the social aspects of textual production and less on the author's intentions alone.