Surrealism's most obvious legacy is a linguistic one. We call on the word "surreal" in response to any situation where the fabulous or the bizarre impinges on our lives, where the boundaries between waking consciousness and the world of dreams seem temporarily blurred. Such occurrences have always been with us, the only difference being that now we have a handy, catch-all phrase with which to indicate and categorise them. That was totally surreal, we drawl, and go back to more pressing tasks. The word has become, in somewhat ironic fashion, merely one more brick in the verbal barrier that we erect against the uncanny.

But the surrealists' aesthetic of estrangement and surprise - inspired, famously, by Lautreamont's "chance encounter, on a dissecting table, of a sewing machine and an umbrella" - has also, to some degree, permeated our whole culture. The casually surrealistic image has become, in particular, a stock-in-trade of the advertising industry. And leaving aside its influence on literature (which has been profound, but necessarily less visible), one could easily mention any number of "surreal" episodes in popular culture. The strange glow that emanates from the briefcase in Quentin Tarantino's Pulp Fiction, to give one minor example, owes its existence to surrealism and the privileged place it gave in art to mystery and desire.

All of this is fairly common knowledge, attested to in almost every recent article occasioned by "Surrealism: desire unbound" at Tate Modern in London. The question most commentators have failed to address is whether this dissemination of vaguely surrealist practice entails the victory of surrealism or its defeat. Has the ordinary truly become surreal, as some postmodernist theorists have claimed, or has the surreal become thoroughly ordinary? Or, to put it another way, have the shock tactics employed by artists such as Rene Magritte and Meret Oppenheim as a means of subverting the hegemony of a rationalist, materialist culture become merely one more element in that culture's increasingly sophisticated seduction techniques? "We must not let the paths of desire become overgrown," said Andre Breton, the movement's spokesman and self-appointed leader. And yet those paths seem choked as never before with vulgarly competing claims on our attention and our wallets. Doubts such as these necessitate a closer look at the movement's actual aims, delving beyond cliched images of lobster telephones and floppy clocks.

What distinguishes surrealism from the numerous other "isms" of the 19th and 20th centuries is the breadth of its field of interest. Unlike, say, impressionism, a specifically artistic movement based on new insights into the operation of the eye, surrealism was nothing less than a philosophy of living. As such, it aimed to transform not merely methods of representation within the privileged realm of the picture frame, but the entire fabric of society. Activities pursued by the artists and poets associated with the movement included film-making, "automatic" production techniques, interrogative sessions aimed at uncovering hidden desires, and - an innovation later adopted by the Situationists - aimless wanderings through the tumult of the modern city. Any representation of surrealism within the confines of a museum, however "enlightened", must therefore be, to a large degree, a falsification of its most radical aspect. The visual arts were only one part of the surrealists' hugely ambitious imaginative project.

Central to their vision of a transfigured society was the concept of desire. In this, they were strongly influenced by Freud's studies of hysteria and repression, a number of which were translated into French in the 1920s. Freud's belief that desire - repressed or otherwise - was the main driving force in our mental lives was gleefully seized upon by the surrealists, who saw in the liberated sexual instinct a force powerful enough to break the stranglehold of the rationalist mindset. The famous concluding line of Breton's novel Nadja - "Beauty will be CONVULSIVE, or it will not be" - alludes directly to Freud's studies of hysteria and repression at the Salpetriere Hospital in Paris, crucial to the development of his theories of sexual repression.

Along with his portrayal of the unconscious as a land teeming with monsters, Freud's ideas inadvertently paved the way for a wholly new (or, depending on how broad your field of vision is, a wholly ancient) conception of art. Ever since the impressionists, modern art had been advancing in quasi-scientific fashion, producing progressively rigorous and schematised abstractions of the visible world. Now the primal forces and uncharted territories revealed by Freud brought a return to more primitive, magical practices. The surrealist artist was not a cool-headed optician concerned with "truthful" representations of reality, but a producer of enigmas, weird visual hybrids intended to shock the mind into sensing the mysteries of existence. What is Oppenheim's famous fur-covered cup and saucer, if not a magical, fetishistic object, a fusion of the apotheoses of civilisation and carnality in a single, unforgettable image? The work of artists such as Salvador DalI and Magritte is similarly disturbing, their fantastical beings and impossible situations depicted with the matter-of-fact technique of the realist painter.

Given the degree of the surrealists' preoccupation with sex, the most fundamentally "magical" of human activities, it comes as no surprise that so much of their art is erotic in nature. Some works, such as Paul Delvaux's paintings of dreamlike cities populated by mysteriously naked women, are more overtly sexual than others. The charge of a picture such as his City With Trams derives from the enigmatic location of the figures, which are themselves drawn somewhat prosaically. Far more typical, however, was the image whose eroticism was veiled, or which worked by means of a kind of visual punning. Aside from Oppenheim's hirsute cup, one could cite the photographs of Man Ray, in which seemingly innocent household implements - a mechanical egg-beater, say - are transformed into aggressively sexual symbols. And then there are the graphic novels in which Max Ernst turned prudish Victorian melodramas into delirious comedies rich with innuendo. Even Lautreamont's chance encounter of a sewing machine and an umbrella on a dissecting table, that image so beloved of Breton, can be read, without too much difficulty, as a wildly graphic description of the sexual act.

What all such images produce is a sense of the mysterious ubiquity of sex, heightening its carnality without losing sight of its strangeness or, crucially, its humorous possibilities. And this brings us directly to the fundamental difference between the society envisaged by the surrealists and our own, a difference that renders irrelevant the supposed surrealism of advertising and the internet. Contemporary culture is no less sex-obsessed, yet cannot seem to see beyond a kind of shallow athleticism that is as impoverished imaginatively as it is worthy and neurotic. In the absence of the transformations of the "surreal" - in whatever sphere of life - one is left with the banality of voyeurism and porn.

"Surrealism: desire unbound" is at Tate Modern, London SE1 (020 7887 8000), until 1 January 2002