Originally founded in 1056 in Skálholt, W-Iceland, it remains one of the oldest institutions of Iceland. The school was moved to Reykjavik in 1786, after having been destroyed by an earthquake. In 1805, however, it was moved once again to Bessastađir, a small town in the vicinity of Reykjavík. In 1846, the school moved to the place where it is now. In 1937 it was given its present name (its old name was Schola Reykjavicensis).

The study is a four years long program, and usually ends with Stúdentspróf, an examination that gives the right to go to an Icelandic university.

The school has approximately 800 students. It is considered hard to get an entrance to MR, and usually only students who have achieved outstanding results in Grunnskóli (secondary school/high school) get in. The school is well known in Iceland for its quality of teaching, and boosts of having won almost every student competitions in Iceland in subjects such as chemistry, mathematics, German and physics. Studies show that MR-students do a great deal better in Universities than students of other schools.

Most Icelandic politicians, including Prime Minister Mr. Davíđ Oddsson and the current and president of Iceland, Mr. Ólafur Ragnar Grímsson either went to MR or taught in it. The only Icelandic Nobel prize winner, Halldór Laxness, spent a few years in MR.