Kulik has authored five books, including Retroverting Slavonic Pseudepigrapha (two editions: Atlanta, GA: Society of Biblical Literature, 2004 and Leiden-Boston: Brill, 2005); 3 Baruch: Greek-Slavonic Apocalypse  of Baruch (Berlin-New York: De Gruyter, 2009); Biblical Pseudepigrapha in Slavonic Tradition (Oxford: Oxford University Press, 2016; with S. Minov); Jews in Old Rus’: A Documentary History (Cambridge, MA: Harvard University Press for HURI, forthcoming); and Jews in Medieval Poland: A Documentary History (Bloomington, IN: Slavica Publishers, forthcoming; with J. Kalik) – and edited seven volumes, among them, the collected volume History of the Jews in Russia: From Antiquity to Early Modern Period in the bilingual series with Zalman Shazar Center (Jerusalem, 2010) and Gesharim (Moscow, 2010) and the Guide to Early Jewish Texts and Traditions in Christian Transmission (Oxford–New York: Oxford University Press, 2019; as editor-in-chief, with G. Boccaccini, L. DiTommaso, D. Hamidovic, and M. Stone).

In 2010, he was awarded the ERC grant ($1.3 million) for the project “Jews and Slavs in the Middle Ages.” Together with Moshe Taube he initiated and led the international research group “Cultural Archaeology of Jews and Slavs: Medieval and Early Modern Judeo-Slavic Interaction and Cross-Fertilization” at the Israel Institute of Advanced Studies in 2011. He directed the German-Israeli Foundation project “Judeo-Christian Encounters and the Last Lingua Sacra of Europe” (with Florentina Badalanova Geller, Rainer Kampling, and Moshe Taube; funded by GIF), “Slavonic Pseudepigrapha in the Intercultural Transmission” (funded by ISF), “The Bible in Russian Modernism” (with Roman Timenchik; funded by ISF). Currently, Kulik is directing the project “Jews in Eastern Europe: 10th-14th centuries” and compiling "The Cambridge Apocalyptic Reader" (with L. DiTommaso). He also founded and headed the Brill book series Studia Judaeoslavica.

Alexander Kulik has held visiting positions at Harvard University, Moscow State University, St. Petersburg State University, University College London, Stanford University, University of Oxford, Université de Lausanne, Freie Universität Berlin, Università Ca' Foscari Venezia, and National Research University Higher School of Economics, Moscow.

Presently, he serves as Professor (previously also Chair) of the Department of Russian and Slavic Studies and Chair of the Academic Committee of the International Center for University Teaching of Jewish Civilization. He holds the Tamara and Savely Grinberg Chair of Russian Studies and is a Member of the International Committee of Slavists.