There are three general histories of classical scholarship in English; all now out-of-date, but still very useful:

• John Edwin Sandys. A history of classical scholarship from the sixth century B.C. to the present day / by . (Cambridge University Press, 1903-1908. 3 Vols. Full-text from the Hathi Trust.
• Ulrich von Wilamowitz-Moellendorff. History of classical scholarship / U. von Wilamowitz-Moellendorff (Johns Hopkins University Press, 1982). Translation, with helpful notes by Hugh Lloyd-Jones, of Wilamowitz's Geschichte der Philologie (Teubner, 1921).
• Rudolph Pfeiffer. History of classical scholarship from the beginnings to the end of the Hellenistic age (Oxford: Clarendon Press, 1968) and History of classical scholarship from 1300 to 1850 (Oxford: Clarendon Press, 1976.

The Oxford Encyclopedia of Ancient Greece and Rome (Oxford, 2010) and Brill's New Pauly (Brill, 2002-), especially the supplements,  includes articles on important topics and figures 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 4th edition (Oxford University Press, 2013)

The history of classical scholarship has often focused on the lives and individual achievements of prominient classicists.
Philologische Biographien (Teuchos) a database based on Eckstein and Pökel.

• Biographical and bibliographical dictionary of the Italian humanists and of the world of classical scholarship in Italy, 1300-1800 / Mario Emilio Cosenza (G. K. Hall, 1962–1967) 6 Vols.
• Biographical dictionary of North American classicists / edited by Ward W. Briggs, Jr. (Greenwood, 1994).
• Classical scholarship : a biographical encyclopedia / edited by Ward W. Briggs & William M. Calder III (Garland, 1990).
• Dictionary of British Classicists / general editor, Robert B. Todd. (Thoemmes, 2004) includes a helpful general bibliography
• The makers of classical archaeology : a reference work / Linda M. Medwid (Humanity Books, 2000).
• Nomenclator philologorum / Friedrick August Eckstein (Teubner, 1871 rpt. 1966). Full-text from the Hathi Trust.
• Philologisches Schriftsteller-Lexikon / Wilhelm Pökel (Krüger, 1882).  Full-text from the Hathi Trust.
  Online continutaion & expansion: Catalogus Philologorum Classicorum (CPhCl)

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.)