The magnificent retrospective of veteran American artist Cy Twombly at London’s Tate Modern is a reminder that, above all else, painting is smearing and drawing is scribble. In his handling, with its extremes of slightness and scatter, informality can border on the infantile.

This show, which is curated by the Tate’s director, Sir Nicholas Serota, travels to the Bilbao Guggenheim in the fall, and then to Rome’s National Gallery of Modern and Contemporary Art, and is the first major survey since the artist’s retrospective 15 years ago at the Museum of Modern Art.

Mr. Twombly, who turned 80 this year, makes big, intellectually ambitious paintings and elemental sculptures that are complex in their interaction with other art and art forms. But he never lets us lose sight of art’s simplest instincts and maneuvers, almost taunting the viewer with the base, raw impulses he lets loose.

His art embraces contradiction. In room after room, this survey offers spare yet dynamic canvases, or cruddy yet evocative sculpture. However nonchalant his painterly marks may seem, they are taut and expressive nonetheless. Scatological as they can be in their oozing and dribbling, his paintings are unfailingly elegant.

There is a dichotomy in Mr. Twombly’s work between the verbal and the nonverbal: Writing is key to his work — often there is text scribbled into his canvases, and titles manifest connections with poetry — but equally vital is a sense that splodges and gestures form an arcane system of pre-verbal expression.

This juggling act, sustained over half a century, is essential to Mr. Twombly’s achievement. But it also accounts for his rocky ride in terms of esteem. Because he taps reserves of brutalism and classicism in equal measure, he is apt to appear too effete to one camp, too grubby to the other. The combination of rough textures and smooth literary references may well account for his greater success in Europe than in America.

And yet, the Americanness of Mr. Twombly’s influences and ambition is as striking as his European refinement. Art historically speaking, he was the kid brother of Robert Rauschenberg and Jasper Johns — he was Rauschenberg’s classmate at Black Mountain College, the legendary North Carolina experimental art college, and later his traveling companion and studio mate. Mr. Twombly offered a similar kind of cool, deconstructive coda to Abstract Expressionism. Early canvases in this show — such as “Criticism” (1955), with its graffiti-like scratching on white house paint — were named at random in studio games with Mr. Johns and Rauschenberg.

In contrast to these peers, however, Mr. Twombly is more an extender than an ender of the AbEx tradition: He literalized the metaphor of handwriting in the free-flowing drips of Jackson Pollock. His work also bears a striking affinity with the late work of Arshile Gorky in the way it joins drawing and painting, each at its most elemental, on the canvas.

From the outset, Mr. Twombly’s touch is unmistakable, and the way he sustains informality on a large scale is prodigious. What is very striking about this show, however, is the diversity of his oeuvre. He anticipates or responds to major stylistic shifts of the last half-century while also retaining his personal idiom.

This is another of his contradictions. He is clearly a fearless individualist, and yet at crucial junctures he seems to have been open to criticism and willing to be swayed. When his opulent, indulgent painterly works from the early 1960s, described as “baroque” and made in borrowed studios in Italy, were dismissed by the Minimal artists who held sway at that time in New York, Mr. Twombly capitulated to the criticism and returned to the austere monochrome of his 1950s abstraction. The pair of massive, multi-paneled canvases titled “Treatise on the Veil” (1968 and 1970) resemble schoolroom chalkboards. The earlier version has a painterly, all-over black ground in oil-based house paint, with markings in white wax crayon sketching out rectangular forms with what look like hastily written calculations and instructions charting a horizontal line toward the bottom of the composition. These minimal works, described in the catalog as an ellipse within the exhibition, could equally be said to act as a hinge between the expressive abundance of the works that preceded and followed.

For soon Mr. Twombly was back on form, indulging his penchant for combining writing and primordial marks in compositions of bombastic lyricism. “Hero and Leandro” (1981-84), a painting in three separate panels, evokes the tragic tale of the drowned lovers in a downward rush of brushmarks that alternate between washed out and globular, fluent and agitated. The name “Leandro” is scrawled with a defiant pity that follows the flow. There is a strong acknowledgement of J.M.W. Turner in the palette and application.

Exalted citations of poetry and classical myth were to prove a compelling influence on the emerging new expressionists of the 1980s, such as Julian Schnabel, Francesco Clemente, and Anselm Kiefer. It is around this time that Mr. Twombly secured his modern-master status in the art world.

A sumptuous work, “Untitled (A Painting in 9 Parts)” (1988), represents the artist at his most traditional-looking, bordering on the Rococo. Shown in the Italian Pavilion of the 1988 Venice Biennale, these paintings, on wood panels, inscribe verses of Rilke in Monet-like feathery and washy applications of oil paint and watercolor, in greens and whites. Two of the panels are elaborately shaped in a way that recalls 18th-century Venetian artists such as Tiepolo.

But in the 1990s, the artist pulled back from this decadent-seeming extreme to reconnect with a more modernist impulse. His “Four Season” cycle (1993-94) explores a lexicon of shapes appropriate to each season, with barely legible tracings of Keats’s poem, “The Human Seasons” (1818), as textual and textural counterpart to these bright colors and expressive gestures.

Mr. Twombly’s sculpture has been a significant part of his output from the beginning of his career, though with a break in production between 1959 and 1976. Made from found objects, which are sometimes cast in bronze, they are typically coated in roughly applied white paint, and they, too, often have writing scribbled into the surfaces. They find the artist in his most archaic mode, and emphasize the brutal, primitive aspect of classicism, as opposed to its refinement. Tomb-like forms such as those in “Untitled (In Memory of Alvaro De Campos)” (2002) are at once elegiac and elemental.

The show ends with a riot of color and lyricism with the “Bacchus” (2005) series. These mammoth canvases reconnect with the pre-scriptural scratched abstractions of the 1950s, while distilling the artist’s lifelong engagement with poetry and myth. In a rich red that hovers between wine and blood, evoking Homer’s “wine dark sea,” these great all-over dripping loops of thick, bold line are marvelously poised between tension and fluency, a final coming together of the artist’s competing impulses to inscribe and describe, to record and to let go.

Until September 14 (Bankside, London, (44) 020-7887-8888).