You may think you know the Tate Modern, which after opening in 2000 on London's Bankside rapidly became one of the world's most popular galleries, but it's time to think again. For Tate Modern had just undergone a major rehang, the first since its move to its former power station home, and for many critics long overdue.

Until now, along with 20 million other visitors to Tate Modern, you have had to choose between themes of landscape, still life, history painting and the nude in order to make inroads into this mammoth collection of modern and contemporary art.

From now on, however, you'll make your way through rooms dedicated to the four main movements, or isms', of modern art Cubism, Surrealism, Abstract Expressionism and Minimalism though not in a chronological fashion. The 48 galleries displaying the permanent collection are still divided into four sections, but now they are called States of Flux' (Cubism, Futurism and Vorticism), Poetry and Dream' (Surrealism), Material Gestures' (Abstract Expressionism and European Informal Art), and Idea and Object' (Minimalism and Conceptual Art).

The idea is to reveal connections between works from different art historical periods, says Frances Morris, Head of Displays. "This is not old wine in new bottles," she stresses. "There is a real sense of discovery about the rehang."

Of almost 400 artworks on view, over 40 per cent never have been shown at Tate Modern before, and 20 per cent are new acquisitions. At the centre of each section display areas or hubs' focus on key innovations in 20th-century art history, and around them satellite rooms, many of which will change annually, show how thinking moves backwards and forwards in time, reflecting earlier artistic practice and shaping later developments.

At the entrance to each section is a dramatic pairing of works by artists from different generations. I loved this idea, finding it effortlessly effective: by relating to each other and the works to come, the pairs provided an exciting introduction to all that followed.

d=3,3,1Take for example Roy Lichtenstein's pop art classic Whaam! made in 1963 and never before shown at Tate Modern. It is paired with Unique Forms of Continuity in Space, a bronze sculpture by Umberto Boccioni conceived in 1913. Boccioni's aerodynamically deformed figure boldly striding towards the future stands frozen in time before Lichtenstein's highly charged, deliberately superficial image of technological power. This wonderful pairing works spatially and conceptually, forming a forceful start to States of Flux', revealing the early 20th century's spirit of change and modernity.

Here is Jacob Epstein's sinister image of mechanised humankind, Rock Drill, created in 1913-14. Here, too, Picasso, Braque, Lger, Richard Hamilton, Damien Hirst and Andy Warhol (including his famous Marilyn Diptych), plus on display for the first time, work by contemporary artists Tomoko Takahashi and the Guerrilla Girls.

Anish Kapoor's new work Ishi's Light stands at the entrance to Material Gestures', paired with two abstract paintings by Barnett Newman. You are invited to go inside the shiny blood-red interior of Kapoor's egg-like structure an odd experience from where you look across to Newman's Adam and Eve on the opposite wall. The stripe of light reflecting off the sculpture's inner wall echoes the vertical bands that are key to Newman's canvases. In both artworks the stripes symbolise the creation of the universe.

Giorgio de Chirico's enigmatic oil, The Uncertainty of the Poet, paired with a Jannis Kounellis drawing covering two walls marks the beginning of Poetry and Dream'. Here you find Magritte's Reckless Sleeper among dozens of surrealist works, and the way the art is dotted around, up and down the gallery walls, gives the room itself dream-like qualities. What you see becomes the scattered visions experienced in dreams: here a skinny walking woman, there a lobster telephone, high up a blue head covered in clouds comes out of the wall (respectively, works by Giacometti, Dali, and Magritte). Soft music adds a finishing touch, unusual to find in a gallery but somehow appropriate here.

The steel and copper tiles of Carl Andre's 1980 Venus Forge lead you into Idea and Object'. Following it, you go underneath a neon sign by Martin Creed that spells out The Whole World + the Work = the Whole World', interpreted as implying either the inclusiveness or the irrelevance of art.

d=3,3,1After Mondrian, Dan Flavin, Hepworth, Beuys, and the ready-made' sculptures of Duchamp and the like, came a room that stopped me in my tracks. Of all the Tate Modern galleries that despite the awful rainy day outside still seem to retain their light and airiness, this was a particularly beautiful space. Minimalist works stood, were hung or dangled here, all of them striking, their geometry corresponding to the space itself; even the ceiling panels high above and the white walls rising up from the art appeared part of the whole. On the floor stood Daniel Judd's gorgeous untitled copper, enamel and aluminium sculpture made in 1972, an open metal box in effect, but its gaping cadmium red interior glowed as materials and colour combined sensuously. Here, too, are Robert Morris's four Mirror Cubes reflecting off each other, causing the viewer to become part of the work, and Carl Andre's notorious firebricks purchased in 1972.

It is not simply novelty that makes this rehang work. Tate Modern seems to have got the formula right. The use of space is better, more contemporary art, women artists, and photography is represented, and it's easier to dip into old favourites and new works and discover connections between them. As Frances Morris says, this hang could not have been achieved in 2000, "The first five years were a sort of laboratory. It enabled us to reflect on what worked, how the audience responded, and take the whole collection forward."

For the events programme that accompanies UBS Openings: Tate Modern Collection' see: www.tate.org.uk