I don’t want to get you too excited, but half the great rehang of Tate Modern’s permanent collection is, um, already hung and available to see right now. Quietly at Christmas, two of the four main areas devoted to the ambitious project were opened. More than 40 per cent of the works have never have been seen before, while 20 per cent are newly acquired. The official unveiling of the rehang (for which The Times is media partner) is on May 23 and is Tate Modern’s first reordering of its collection since it opened in 2000. Since then, annual visitor numbers have settled at a record-breaking four million.

Gone are the old themes — “The Landscape”, “Still Life”, “History” and “Nude” — to be replaced by “Poetry and Dream” (Surrealism and “Surrealist tendencies” — which sounds slightly pathological); “Material Gestures” (Abstract Expressionism and European Informal Art); “States of Flux” (Cubism, Futurism and Vorticism); and “Idea and Object” (before and after Minimalism).

The pictures that people will flock to see — Roy Lichtenstein’s Pop classic Whaam! and Andy Warhol’s Marilyn Diptych — are up on floor five in “Flux”. The idea is to thread your way between rooms, arranged by theme, not time. So far the rehang is more or less complete on level three (when you alight from the escalators go straight ahead for Abstract Expressionism or double back on yourself for Surrealism).

In the entrance of each room stand a couple of works that are intended to “echo” each other. According to Frances Morris, head of displays at Tate Modern, the intention of opening the rooms in this way is to highlight the “ongoing relationships” between artists from different periods.

Announcing the rehang last autumn, Sir Nicholas Serota, the gallery’s director, said he “would be surprised” if there was no criticism of the gallery’s decision not to exhibit the works chronologically. “Our purpose is not to deflect criticism, but to present the collection in the strongest possible way.” Morris claims that a chronological history isn’t useful. “The development of artistic practice takes place in moments in time, dialogues over time, how the perspectives of the past form antecedents to the present. The intention is to provide an overview of art history for the broadest possible audience, so they can see those moments when the game changed, when paradigms shift, while seeing how artists through time became fellow travellers, or overtly rejected one another’s ideas.”

After the opening two artworks, you move to a central “hub” which acts as a kind of bran-tub of different artworks related to that genre, with rooms devoted to single artists, or artists the curators think relate to one another, heading off that.

POETRY AND DREAM

This journey around Surrealism opens with Giorgio de Chirico’s classic The Uncertainty of the Poet, featuring a bust, a train and bunch of bananas (all configured out of scale), next to a mammoth installation by Jannis Kounellis comprising stuffed birds skewered to the wall by paper arrows against a background of spindly houses. De Chirico and Kounellis never met, but in bringing them together Tate Modern seeks to illuminate the roots of Arte Povera, the Italian art movement that embraced found materials above paint; and there is also the neat concordance that de Chirico was an Italian artist who lived in Greece while Kounellis, a Greek, lived and worked in Italy.

The Surrealism hub features Dalí’s Lobster Telephone, some amazing Man Ray pieces and Magritte’s Reckless Sleeper. In subsequent rooms you come across Cy Twombly’s exercises in stone sculpture contrasted against the most wonderful, monumental Joseph Beuys sculpture, Lightning with Stag in its Glare, in which a rough-hewn bronze triangle doubles as a streak of lightning looming menacingly above an ironing board artfully made up to look like a stag. A cast of bright aluminium stands as the glare of the lightning. In another room some work by Louise Bourgeois, most notably a new acquisition, Mamelles — a bulbous, pink cast made up to look like a line of breasts — stands next to some vintage Francis Bacon paintings of fractured, atomised bodies. The idea here is to focus on two artists who, in their own very different ways (Bourgeois, now 94, has often cited Bacon as an influence), are obsessed by the disintegration of the body.

MATERIAL GESTURES

To kick off this sweep through postwar art, a couple of Barnett Newman canvases sit alongside the first fun contraption of the rehang, the newly acquired Anish Kapoor’s Ishi’s Light (named after Kapoor’s son Ishan and inspired by Newman). It’s an upturned shell that disorientates you as you step inside. The hub consists of a Rothko room, a melange of Monet and Matisse and the recently rediscovered American painter Joan Mitchell (one of the interesting aspects of the rehang is the attempt to give long-ignored notable women artists their moment).

In the same room, the Wrong Gallery, says Morris, is “a spanner in the works, a parasite in our midst”. Her twinkling eye suggests this is the art gallery equivalent of a parent sighing over a teenager’s messy bedroom. Wrong’s pornographic installation is as close to overtly controversial as the rehang gets. A kitschly painted naked woman (with a real head on a video screen) mouths goodness-knows-what-but-it-sounds-orgasmic in an installation by Dorothy Iannone. When I was there, someone tutted “That’s disgusting” while some teenagers giggled and checked out the painted lady’s private parts.

Tacita Dean’s The Roaring Forties: Seven Boards in Seven Days is a series of mesmerising floor-to-ceiling blackboards with chalk drawings of an ill-fated sea voyage. Dean was inspired by Donald Crowhurst, who made up co-ordinates and eventually committed suicide during a round-the-world yacht race in 1969. On the landing, UBS, which has put up much of the cash for the rehang (the Tate won’t say how much) has a mini-gallery devoted to showing its own art.