Galleries on the main floor are devoted to a temporary exhibition of recent works by Twombly, as well as film, video, and photography, but the survey begins two flights up on the third. Installed roughly in chronological order, the works tell the familiar story of modernism and postmodernism, from Cubism to Koons and beyond, but a number of curatorial surprises give the conventional riff new life. At the entrance, three representations of the eternal feminine from the last century make up a lusty welcoming committee: Henry Moore’s big bronze maquette for a reclining figure (1957) and two paintings: Picasso’s Portrait of Sylvette David (1954) and Matisse’s huge Bathers by a River (1917). The generously proportioned rooms contain pleasures at every turn, like Brancusi’s little-known sculptures Two Penguins (1911–14) and Wisdom (1908) and Russian Futurist Natalia Goncharova’s Spanish Dancer (1916), an elegant conflation of folk art tradition and religious icons. Even old chestnuts have never looked better: Dali’s Venus de Milo with Drawers (1936) is still sexy and startling, and Magritte’s Time Transfixed (1938), a locomotive busting out of a fireplace, shows an overexposed Surrealist in top form.

One of the greatest delights on this floor is the intact Lindy and Edwin Bergman Collection, a quiet haven of interior galleries that includes a wall of 38 Joseph Cornell boxes, a beguiling little predator bird from the late French sculptor Germaine Richier, and a gouache on corrugated cardboard that leaves you guessing the artist until you look at the label (it’s Picasso).

The second floor picks up with art from 1950 to the present, and here the curatorial thinking is abuzz with clever juxtapositions. A room of paintings from contemporary artists Lucian Freud, Lisa Yuskavage, Margherita Manzanelli, and Luc Tuymans gives a nod to the ongoing tradition of figurative painting. Kerry James Marshall’s homage to Fragonard’s The Swing is laugh-out-loud funny, especially when considered in tandem with Robert Gober’s deadpan objects and wallpaper. Eva Hesse and Richard Serra share a gallery, showing the masculine and feminine sides of Minimalism, and pairing Roy Lichtenstein with Andy Warhol reconsiders Pop art’s chillier moments. The museum has also given special consideration to the city’s homegrown talent, with a gallery devoted to Jim Nutt and a creepy Ed Paschke painting of a boxer glowering at Jeff Koons’s porcelain Woman in Tub.

Several great landmarks from the 1950s, such as de Kooning’s Excavation and Joan Mitchell’s knockout City Landscape, are reminders of Abstract Expressionism’s ongoing power, but Color Field painting is almost entirely slighted, the exception being a pale Sam Francis canvas that seems like a hasty afterthought. Occasionally works are sited in alcoves — like Francis Bacon’s Figure with Meat (1954) or Martin Puryear’s Sanctuary (1982) — as if they don’t quite fit with the story line, but the placement also asks viewers to consider the rich individual detours from the movements that dominated the last century.

Regrettably, other galleries don’t quite yet hold their own against the strengths of the painting and sculpture collection. Twombly, in the Abbott Galleries for Special Exhibitions, is still going strong at 81, but he has produced better work than this. The Ellsworth Kelly sculpture in the Pritzker Garden looks lonely and purely decorative, and the spaces devoted to architecture and design are letdowns after the high level of curatorial panache elsewhere. But a new addition of this kind has to be an organic and malleable work in progress. Let’s hope that future tweaking will bring stronger contributions and fresher thinking to the smaller attractions as well as the main event.