Reichman considers himself primarily a student of the twentieth century Talmudic genius Rabbi Joseph B. Soloveitchik.
However, Reichman officially received his rabbinical ordination (semicha) from Rabbi Moshe Feinstein, with whom he studied Jewish Law in a private tutorial.
Reichman became the newest member of the Rabbi Isaac Elchanan Theological Seminary faculty to occupy an endowed chair when he was invested by President Richard M. Joel as the Bronka Weintraub Professor of Talmud on September 18, 2006 in the Harry Fischel Beit Midrash of Zysman Hall on the Wilf Campus.
After World War II, Reichman's grandfather served as an emissary of the Belzer Rebbe, Rabbi Aharon Rokeach.
The younger Reichman has written a book about Hasidic thought called Flames of Faith: An Introduction to Chassidic Thought, adapted from the Torah classes of Rabbi Moshe Wolfson, and has translated the book Haser Ka'as Milibecha, under the title Remove Anger from Your Heart.