The Ludwig story begins, in a sense, in 1946. A Cologne lawyer named Josef Haubrich had spent the Nazi years quietly holding onto Expressionist paintings the Reich had branded "degenerate art" — Erich Heckel, Karl Schmidt-Rottluff, Ernst Ludwig Kirchner, August Macke, Otto Mueller — and in the smoking ruins of the immediate postwar months he handed his entire collection to the city as a gift. That became the Sammlung Haubrich. Three decades later Peter Ludwig, the chocolate industrialist, and his wife Irene added their own collection of Picasso, Russian avant-garde, and American Pop Art. The museum that grew up around these two donations opened to the public in 1986. It shared its building at first with the older Wallraf-Richartz Museum, but by 1994 the two had divorced and Museum Ludwig had the place to itself.

About 900 Picassos. The number is staggering. Only Barcelona and Paris hold more of his work, and Ludwig got there because Peter and Irene kept feeding the collection back to the city for decades. The Russian avant-garde holdings are almost as remarkable: 600 works from the years 1905 to 1935 on permanent loan, including pieces by Kazimir Malevich, Ljubov Popova, Natalia Goncharova, Mikhail Larionov, and Alexander Rodchenko. Outside of Russia itself, no museum in the world holds a more comprehensive collection of those early revolutionary years in Russian art. Then there is the Pop Art floor — Warhol's Race Riot and Two Elvis and the 80 dollar bills; Lichtenstein's Takka-Takka and M-Maybe; Rauschenberg's Odalisque and Black Market; Claes Oldenburg's giant soft sculptures of plain American things.

The museum building has a peculiar tenant beneath it: the Kölner Philharmonie, Cologne's concert hall, occupies the basement levels. Above the orchestra's roof is the Heinrich-Böll-Platz, a public square designed by the Israeli artist Dani Karavan and named for Cologne's Nobel-laureate novelist. The acoustic quirk of this arrangement is genuinely strange. During concerts, footsteps on the plaza above leak into the hall below as a low rumble, so guards are stationed at the entrances and visitors must wait until the music stops before they can cross. For roughly half the hours of the year, a square in the middle of Cologne is closed to its own city for the sake of a string quartet playing twenty metres beneath the pavement.

The museum has tried, sometimes belatedly, to reckon with the way Nazi looting shaped European collections. In 1999 it returned an Otto Mueller painting to the heirs of the Jewish lawyer Ismar Littmann. In 2000 it returned a Louis Marcoussis canvas to the family of El Lissitzky and his widow Sophie Lissitzky-Küppers. Five drawings by Kirchner, Heckel, and Georges Kars went back to the heirs of Curt Glaser. A different kind of trouble befell the wider Ludwig family of museums in 2016, when the Ludwig Museum in Koblenz co-organised an Anselm Kiefer retrospective that travelled to China. The exhibition's final stop was supposed to be the new Jupiter Museum of Art in Shenzhen, but when that museum's opening was delayed the works went into storage and the Koblenz museum lost track of them. In January 2020 staff located six paintings, including Kiefer's monumental Pasiphae, sitting in a warehouse — only to be blocked from retrieving them by Chinese authorities. After diplomatic intervention by the German government and the City of Koblenz, the works were returned safely in August 2020.