Built in 1878-81 by the architect H.B. Storck in Renaissance style. It replaced the Baroque church built after the fire of 1728. The earlier Gothic church dated from c.1400, and the later church is built on the old foundations. The oldest part of the church today is the south portal (third and fourth pictures) which is genuine Renaissance, a gift from King Christian IV in 1630. The tower is a reconstruction of  Hans van Steenwinckel's tower of 1582-94.
Storck's church is six bays long with depressed round-arched windows and with buttresses between. It is almost identical to an engraving in Erik Pontoppidan's "Danske Atlas", vol. 2, København 1764, although that has no ridge turret nor ornamental gables. It shows the west entrance portal in the west-most bay of the south facade, with a shortened window above.

A choir of two bays and three-sided east end. Two additions on the north side, the second a half onion-domed building with oval windows which is Griffenfeld's chapel of 1673, designed by Lambert van Haven.

A monastery was built beside the church in the late 15th century of which the Gothic west wing is preserved. Known as Helligåndshuset (Holy Spirit House) it is the most intact large medieval building in Copenhagen.

Storck's interior. The church is a three-aisled basilica under a single roof. Two large chandeliers of the 17th century. The pulpit is from 1879 but was modelled on early 17th century pulpits. The crucifix to the right of the pulpit was carved in 1969 by Henrik Starcke from a single piece of bog-oak. The Baroque altar piece with the painting of the Ascension by Hendrik Krock is from 1727. The marble font was made in 1827 by Bertel Thorvaldsen while in Rome, it went from there to England and then to Denmark in 1938.

From the altar, looking west. Under the organ, a painting of the Annunciation from 1897 by Joakim Skovgaard .