"[2] Founded in 1996 by graduate students Ben Karp, Noah Feldman, Michael Alexander, future senator and presidential candidate Cory Booker, and Rabbi Shmully Hecht, the society was formed to bring together Jewish and non-Jewish leaders on Yale's campus in an intellectual salon setting influenced by secular and religious branches of Judaism.

[3] The society hosts weekly Shabbat dinner meetings in New Haven, featuring a discussion-based format and an ethos of mutual improvement that has been likened to Benjamin Franklin's Junto Club.

As one journalist described it, "like Yale's famous secret societies, Shabtai is elite and exclusive, but unlike the infamous Skull & Bones or Scroll & Key or Book & Snake, it is not clandestine.

"[4] Another described it as facilitating "the kind of conversations around the Shabbat table that bring together secular and sectarian, poor and rich, Muslim and Jew, student and scholar, Mormon and pagan and jock and genius.

[7] The society hosted Tony Schwartz, ghostwriter of The Art of the Deal, in 2017 to discuss Donald Trump's psychology, motivations, and character, as observed from shadowing him to write the book.

[8] In November 2018, Shabtai hosted criminal justice reform advocate Anthony Ray Hinton at a Yud Tes Kislev event commemorating the anniversary of the release of Shneur Zalman of Liadi from imprisonment by the tsarist Russian police.

These have included David Brooks, Timothy Snyder, Anne Applebaum, James Kirchick, Bret Stephens, Bari Weiss, Elizabeth Wurtzel, Leslie Epstein, Dovid Katz, Ed Rothstein, Joshua Safran, Peter Salovey, Adam Gopnik, Joseph Klein, Jeremy England, Eben Alexander, Scott J. Shapiro, Lara Vapnyar, Andre Aciman, Christine Hayes, Kathryn Lofton, Graeme Wood, James Dao, Trish Hall, Stephen Carter, Keith Urbahn, Steven B. Smith, Jack Balkin, Laurie R. Santos, Charles Hill, Kate Stith, Louis Begley and Jay Winter, Mark Weitzman, Dave de Jong, Nikolay Kapasov, David Marwell, Joyce Maynard, Jessica Roda, Zvi Kolitz, Sherwin B. Nuland, Nir Navon, Brad Innwood, Will Eisner and Beth Kobliner.

These have included Adin Steinsaltz, Ephraim Mirvis, Yanki Tauber, Tzvi Freeman, Emanuel Rackman, Sholom Dovber Lipskar, David Lincoln, James Ponet, Levi and Bassie Shemtov, Jacob Immanuel Schochet, Harry Ballan, Asher and Sarah Esther Crispe, Mark Oppenheimer, Matt Nosanchuk, Yitzchok Kogan, Y.Y.