The name Rubens tends to conjure visions of plump nudes, displaying an abundance of opulent flesh. This is both fair and unfair.

The great baroque Flemish painter Peter Paul Rubens (1577-1640) did indeed paint plump nudes, or nearly-nudes, but they are only one facet of this astonishing artist's range of subject matter and massive output.

He is in a sense a painterly version of Shakespeare, dominating not only his own contemporary art world but influencing subsequent generations of Continental and British artists up to the present day.

A splendid exhibition - at the Bozar Centre for Fine Arts, Brussels, till January 4 and opening at the Royal Academy, London, on January 24 - sets out to examine both this creative Titan's own work and his influence on others. The Brussels exhibition has the rather titillating main title of 'Sensation and Sensuality'. The London version more soberly opts for 'Rubens and his Legacy'.

Forget the Seven Deadly Sins. Here the subject matter is divided into six themes - Violence, Power, Lust, Compassion, Poetry, and Elegance.

In Brussels the visitor plunges headfirst into Violence, with big-game-hunting, grim scenes of the sinful tumbling into hell (rather detached from their religious significance), and some classical rapine thrown in the mix.

Rubens's own Tiger, Lion and Leopard Hunt, c1617, dominates the scene with its bravura central image of the rearing white horse with rider unseated by the tiger clamping its jaws on his shoulder. Delacroix and Sir Edward Landseer are among the many imitative successors who cannot match the savage energy.

The Power section is interwoven with the artist's own life spent mingling diplomatically with royalty and nobility on the Continent - and Stuart England (Rubens was knighted by Charles I).

For anyone brought up on the historic romances of Alexandre Dumas (Pere), the images from a series of paintings commissioned from Rubens by the widow of Henry IV of France (he who thought Paris "vaut bien une messe), may have special interest. Maria de Medici wanted one set to represent her "famous life and heroic actions." No question of modesty in those times when the divine right of kings (and queens) was the prevailing orthodoxy.

Piquantly, Rubens was also commissioned to paint ceiling pictures for the Banqueting Hall in Whitehall. The Apotheosis of James VI and I still graces the great space, showing the foreshortened monarch looking vaguely comical, as he tilts backwards. The religious-cum-political context must have seemed strange in seventeenth-century England with its democratic upheavals. Charles I walked out of a window of the hall to his execution in 1649. Images for the commission are included in the Power section of the exhibition.

Strangest of all in this section is a canvas by Oskar Kokoschka, painted as an allegory during the Second World War and mocking Britain's lost maritime supremacy, with an image of Queen Victoria feeding seamen to a white shark. A painting as crudely executed as its message.

And so to Lust. This will, one suspects, be the most popular section of the exhibition.

Rubens's nudes and their successors are here in all their corporeal splendour. The most exquisite of them is Venus Frigida (dated 1614). The crouching Venus, not frigid in the sexual sense but, rather, feeling the cold, is seen from the side; her profiled face, framed by blond hair, has a preoccupied expression. Her body is not too heavy and her skin radiates both luminous beauty and underlying anatomical subtlety. Crouching at her feet is a crabbit Cupid, and bearing food and drink is one of the Satyr figures who seem to be an indispensable part of this genre of painting.

The theme of woman and lascivious male is central to various fascinating paintings, including Pan and Syrinx, on which Rubens collaborated with Jan Brueghel the Elder. In the setting of a reed-bed, the nymph Syrinx - a much beefier figure than Venus - displays a surprisingly tranquil expression as the Neanderthal-like Pan tries to twitch off her minimal clothing. She is saved by being transformed into a reed. Exquisite symbolic flowers add to the scene.

There are various voyeuristic canvases of sleeping women menaced by ugly male figures - a Rubens hermit and sinister Jupiter by Van Dyck included. The intention of rape is implicit as the males tug at the vestigial garments of the sleeping women. Did putting these scenes in a mythical context make them acceptable to puritan sensibilities? They certainly make rather uncomfortable viewing today, as do later interpretations of the theme by artists such as Rembrandt, Watteau, and Picasso. (Why can't the poor women at least have had some good-looking predators?)

Emotions of a more elevated kind are depicted and demanded in the Compassion section. This could have been labelled more straightforwardly as Religion. Rubens painted his religious pictures, especially scenes from the Cross, in the high days of faith and Counter-Reformation. To look at them with the detached response of the non-believing or in purely aesthetic terms is unfair to their genesis.

Among his masterly depictions of the ascent to and descent from the Cross, Christ on the Straw (1617-1618) is particularly haunting, thanks to the glazed, agonised, face of Christ himself, and the visual pain of those surrounding him. The influence of this central aspect of Rubens's oeuvre stretched as far as Landseer and Gainsborough.

After the high and low emotional tensions of the previous sections, the exhibition enters the calmer waters of Elegance and Poetry. Rubens was a consummate portrait painter, as his self-depiction with his first wife Isabella Brant demonstrates. Caught in a honeysuckle bower, the opulently dressed and handsome couple - she with her ruff and high hat, he with his romantic whiskers, and lace collar - radiate confidence and prosperity. This painting is a reminder of what a successful artist in worldly terms Rubens was - a fact proved, if proof were needed, by his mansion house, complete with formal garden and statuary, in Antwerp.

His pupil Van Dyck, favourite portraitist of the Stuart court, and succeeding generations of English artists such as Reynolds, Gainsborough, and Lawrence, join Watteau, Fragonard, and Elisabeth-Louise Vigee-Lebrun in showing his influence. One delightful Rubens portrait, Chapeau de Paille, has the feminine softness and charm of a Renoir.

Was there no area of painting in which Rubens didn't excel? The landscapes of his later years - for example A View of Het Steen in the Early Morning (c1636) and Landscape with Moon and Stars (1637-38) - deserve the description of visual poetry. They carry intimations of Constable and Turner.

There will be an additional section at the Royal Academy. Under the title La Peregrina, Jenny Saville, RA and Glasgow Art School graduate, will offer a contemporary response to the themes in the Rubens exhibition, curating a display of works by leading twentieth and twenty-first century painters, ranging from de Kooning and Picasso to Francis Bacon and Lucian Freud. Saville, known for her painterly preoccupation with flesh, will also be creating new work for the occasion.

Rubens and His Legacy is at the Royal Academy of Arts, London from Saturday, January 24 to Friday, April 10.