There are three general histories of classical scholarship in English, all now out-of-date, but still very useful:
The Oxford Encyclopedia of Ancient Greek and Rome (online) (Oxford, 2010) includes articles on important topic and figure in the history of classical scholarship.
Also very useful is L. D. Reynolds and N. G. Wilson's Scribes and scholars : a guide to the transmission of Greek and Latin literature 3rd edition (Oxford University Press, 1991)
The history of classical scholarship has often focused on the lives and individual achievements of prominient classicists.
Classical periodicals will often contain obituaries of recently deceased classicists. They were a regular feature of "Bursian's" Jahresberichte über die Fortschritte der classischen Altertumswissenschaft (1873–1956), and continue in Gnomon (1925–) now in JSTOR. Additional material can be found in L'Année Philologique indexed by the subject heading X.Festschriften and Proceedings D. Personalia (beginning with volume 67, before that under X.Festschriften and Proceedings: Necrology.)