THERESA THOMPSON visits the exhibition at the Tate Modern that celebrates the American artist Cy Twombly in his 80th year

Cy Twombly is 80 years old this year. Tate Modern celebrates the American artist's birthday with the first major survey of his work in the UK for 15 years, bringing together paintings, sculptures and drawings to provide an overview of his work from the 1950s to the present day.

Cy Twombly: Cycles and Seasons is less a complete retrospective, says Tate director Nicholas Serota, who curated the exhibition, than a survey. Featuring 107 works, it is structured around key periods in Twombly's long career and certain strong themes, such as time passing, love, doomed desire, water, and a poetic sense of history steeped in the classics.

He frequently works in cycles. One of which, begun in 1991 when living in Bassano, Italy, Quattro Stagioni (Four Seasons) is a sublime painting in four parts that you may already be familiar with from the Tate. Here in the show it is reunited for the first time since leaving Twombly's studio with a similar, if sparser, version from the Museum of Modern Art, New York. These huge canvases, made when he was approaching his mid-sixties, loosely follow a classical tradition in which each painting of a season - titled in Italian Primavera, Estate, Autunno, Inverno - also represents a different stage in life.

In each painting different colours register the changing light and temperature of the seasons. Spring shows itself to be young and vital, full of growth, with vertically placed splashes of fresh yellow and bright red; Summer is sensual, transient, with hazy yellows and creams as if from a blinding sun; Autumn is torpor, stained with the purple blush of wine and fruit, invoking Bacchus perhaps with its scribbled phrase Your blood'; and Winter, with death encroaching, has words disappearing under a wall of ice, loomed over by dark fir-like shapes, laden with snow. Spring is also violent; the curves apparently are Egyptian-style boats, traditional war canoes.

Boats appear in a number of Twombly's works, including some sculptures on display, transporting us from one part of life to another. Water is another common theme.

Born in 1928 in Lexington, Virginia, and studying in Boston and New York at the height of Abstract Expressionism, Twombly is one of the leading figures of a generation of artists that includes Andy Warhol and Jasper Johns. He met Robert Rauschenberg in 1950, sharing a studio with him in Manhattan from the mid-1950s. The period saw him fuelling his interest in calligraphy and the automatic drawing processes of the surrealists.

Twombly first went to Europe in 1952 on a travelling scholarship, and then followed Rauschenberg to Morocco. He moved to Italy in 1957 where he has stayed for much of the time since, his imagination fired by the colours of the Mediterranean, European literature and classical mythology. Gradually he developed his unique style that seems to combine Jackson Pollock's expressiveness with a romantic tenderness, graffiti art with erudition: it's a world away from the tough, aggressive tradition of American art.

Words began to appear in his paintings in the 1950s, dense pencil scribbles at first, later phrases, sometimes legible, sometimes not; numbers soon joined them, titles, signatures too. Interestingly, when drafted into the army in 1953 he worked on cryptography.

"One criticism I've heard of him is that he is too erudite," Serota said. "He spends a great deal of time reading. He is inspired by poetry and literature, writing down a line or phrase that has particular resonance to keep until he uses it.

"But why not use poetry?" he asks. "Why should one feel defensive about something that gives so much back to us? Some of the most difficult art is that which stays longest with us."

His are majestic, exuberant works that are both abstract and literary. Though at times difficult, to my mind their sensuality rewards efforts made.

It will take a devotee, however, to look that closely at the many similar works in the opening rooms, apart from the dramatic few at the entrance. But the predominantly black-and-white art, the blackboard-like Treatise on the Veil, for instance, provides a right and proper build up to the tremendous bursts of colour and emotion that come later in this broadly chronological show.

The Hero and Leandro (1981-4) triptych is shown beside a small panel with a line from Keats scrawled on it. Based on the classic tale of doomed love as Leandro (Leander) dies swimming across the Hellespont to Hero, his lover, Twombly evokes the tragedy using waves of brush strokes cascading across the canvasses, flattening out, becoming emptier, thinner as the passion dies. I found it immensely powerful.

Several key series are reunited for the first time here, including his Ferragosto paintings from a red-hot stay in summertime Rome in 1961, the nine watery Green paintings from 1988, and the gigantic Bacchus series of violent vermilion swirls made in 2005 that show the artist is as vigorous as ever.

"Painted in 2005 with a brush on the end of a pole, not unlike Matisse," said Serota, "these enormously energetic scrolls of paint on canvas take us back to the kind of mark-making we saw in his early work at the beginning of the exhibition."

Cy Twombly: Cycles and Seasons is at Tate Modern until September 14. For details visit the website www.tate.org.uk/