These are the open access eJournals (or components thereof) focused on reviews of books on the ancient world of which I am aware. Are there others? Please let me know.
- Aestimatio: Critical Reviews in the History of Science
- American Journal of Archaeology Book & Museum Reviews
- The Ancient History Bulletin Online Reviews
- Археология (Reviews and News are open)
- Arctos: Acta Philologica Fennica - Reviews
- Bryn Mawr Classical Review (BMCR)
- Digressus: The Internet Journal for the Classical World
- Dissertation Reviews
- Histara-les comptes rendus: histoire de l'art, histoire des répresentations et archéologie
- Marginalia: A Review of Books in History, Theology and Religion
- The Prehistoric Society: Book Reviews
- Review of Biblical Literature (RBL)
- Ride: A review journal for digital editions and resources
- Scholia Reviews
- Teiresias: A Review and Bibliography of Boiotian Studies