The museum comprises three permanent collections whose nucleus dates back to the days of its founder, C. L. David: the Collection of Islamic Art, the Collection of European Art, and the Collection of Danish Early Modern Art.
The Collection of Islamic Art – internationally, the museum’s most important one – encompasses exquisite decorative art from the 7th century to the mid-19th century from an area that extends from Spain in the west to China in the east, from Uzbekistan in the north to Yemen in the south.
The Collection of European Art features a rich selection of art from the 18th and 19th centuries: furniture design, French and German porcelain, Danish faience and silver, and Danish, Dutch, and French paintings.
The Collection of Danish Early Modern Art comprises paintings and sculptures made by Danish artists between c. 1880 and 1950. Until September 2018, only work by Vilhelm Hammershøi is on display.