It was used initially when Althing began to meet again in Reykjavík after a few years hiatus and thus it is in this building where Icelandic independence leader Jón Sigurðsson led the MPs in their famous phrase, Vér mótmælum allir.

It usually ends with a degree (stúdentspróf) which gives the graduating student the right to advance to an Icelandic university.

Many Icelandic politicians, including the first prime minister Hannes Hafstein, former Prime Minister Davíð Oddsson, former President of Iceland, Ólafur Ragnar Grímsson and current president, Guðni Th.

Almost every Prime Minister of Iceland has been educated at the school apart from Halldór Ásgrímsson, Ólafur Jóhannesson, Sigurður Ingi Jóhannsson, Þorsteinn Pálsson, Jóhanna Sigurðardóttir and Katrín Jakobsdóttir.

In 1879 Hannes Hafstein was the school's first inspector scholae, and in 1940 his grandson Einar Ragnarsson Kvaran achieved the position.

Every year at the end of spring semester the students of MR organize a fight in the halls of the main building.

This event was cancelled permanently after the 2008-2009 Inspector Platearum (a senior student who is responsible for ringing the school bells and is furthermore the leader of the seniors in the Hall Fight) broke his neck in the fight, resulting in a 9 million ISK lawsuit.

The day starts with the seniors dressing up in white toga cloaks and painting their faces.

The tradition of throwing newcomers into the air is old - but the part of dressing up in toga was added by seniors in 1991 (graduating in 1992).

"Framtíðin" administers the debating society for MR students and it is also one of the oldest clubs in Iceland (founded in 1883).

Another annual competition is held, called "Orator Minor" (Latin: The next-best spokesman).

Orator Minor is a competition where people debate about randomly selected subjects in one-on-one battles and only have ten minutes to prepare their speeches.

MR has been the most successful school on RÚV's academic quiz competition Gettu betur; it has been champion in 23 series of the programme, with its most recent occurring in 2023.

One day in October each year, the students of MR and its rival school, Verzlunarskóli Íslands (Commercial College of Iceland) or "Verzlo" as it is often referred to as, meet in the "Hljómskálagarður" park, located in downtown Reykjavík, where various games and competitions are held.

These include: sprinting, soccer, rowing, giant-chess (later replaced with ordinary chess), screaming, tug-o-war, competitive eating, arm wrestling, car stuffing and the infamous Mexican-run.

MR offers two separate "paths" which students choose when enrolling in the school.