It was originally located on the Lower East Side, and moved to Washington Heights with the rest of Yeshiva in the late 1920s.

However, with the growth of competing institutions, enrollment declined, and by 1999, Rabbi Dr. Norman Lamm, President of Yeshiva University, wanted to close the high school down.

When word of the closure leaked out, Rabbi Michael Taubes, MTA's principal at that time, together with senior instructor, Rabbi Yitzchok Cohen, led a student protest and recitation of Psalms in front of the YU's main building at that time, Furst Hall.

In February 2011, Rabbi Mark Gottlieb announced that he would be stepping down as Head of School/Menahel at the culmination of the 2010-2011 academic year.

His successor was former principal Rabbi Michael Taubes, who took over as Head of School (now also known by the Hebrew title of Rosh HaYeshiva at the start of the 2011-2012 academic year.

The alleged misconduct, which occurred during the 1970s and 1980s, was claimed to have been known about, but ignored, by the highest levels of administration at the high school and at Yeshiva University.

The story alleges that the door to one of the abuser's offices was removed to prevent a private environment where further misconduct could continue.

[7] The lawsuit against Yeshiva University was dismissed before trial in January 2014 by a federal judge who stated that the statute of limitations had expired.

In other areas, there are College Bowl, Torah Bowl, Mock Trial, Model UN, Model Congress, Chess, Debate, MTAhackers (the high school team won the 2022 university hackathon[10]), a 3d printing club, a Math team, as well as the Business is Booming and Finance Club.