Twersky succeeded his father Meshullam Zalman Twersky as the Talner Rebbe of Boston for the last twenty years of his life, serving as the spiritual leader of Congregation Beth David, known colloquially as the Talner Beis Medrash ("the Talner study hall"), which was located in a renovated house in the Brighton neighborhood of Boston. Twersky's lectures in the synagogue on Tuesday nights and late Saturday afternoons were known for their erudition and originality, in the tradition of elite religious Torah study, with the vocabulary and worldliness of a Harvard historian. Twersky and his wife Atarah (née Soloveitchik) played a prominent part in the leadership of Maimonides School. Twersky took on the role of spiritual leader for the school in 1993, after the death of Atarah's father Joseph B. Soloveitchik, who had founded the school in 1937. Atarah was the long-time chair of the School Committee, until 2006, nine years after Twersky's death. The Twersky's elder son Mosheh, a rabbi and lecturer at Yeshivas Toras Moshe, was murdered in the 2014 Jerusalem synagogue attack. Their other son Mayer Twersky holds the Leib Merkin Distinguished Professorial Chair in Talmud and Jewish Philosophy and is a rosh yeshiva at Yeshiva University and rabbi of the Talner Synagogue of Riverdale. Their daughter Tzipporah Rosenblatt, a lawyer, is married to Jonathan Rosenblatt, rabbi emeritus of the Riverdale Jewish Center in New York City. Atarah resides in Riverdale.