It runs from Købmagergade in the northeast to the Church of the Holy Ghost in the southwest where it makes a sharp turn left to join Strøget.

The section from Købmagergade to Niels Hemmingsens Gade was originally called Store Helliggeiststræde (Large Alley of the Holy Hjost).

The first part of the name distinguished it from Lille Helliggeiststræde (Small Alley of the Holy Ghost) which was the name of Niels Hemmingsens Gade at that time.

It was almost completely destroyed in the Copenhagen Fire of 1728 but rebuilt shortly thereafter by J.Johan Cornelius Krieger.

The building was designed by Theodor Zeltner in a style that matches the Baroque architecture of the main wing.