Christian Louboutin, Design Museum, London

But they are designed to transport wearer and onlooker alike into a world rich with suggestion

Louboutin flash: the designer recently tried - unsuccessfully - to stop other makers using his signature red sole

When talking of high heels, it's as well to define terms. There are the sort that Marilyn Monroe wore to wiggle along that railway platform in Some Like It Hot. There are the sort that Strictly dancers wear to sharpen their silhouette. And then there are the ones that cause young women to clutch each other for support in the street on a Saturday night, bracing their knees and arching their backs in the attempt to keep upright.

It's largely shoes like these – but very expensive ones – that have kept the Parisian Christian Louboutin in business for the past 20 years, and now the Design Museum has devoted an exhibition to them. It presents an interesting conundrum. If the same museum were to mount an exhibition of, say, vacuum cleaners that didn't pick up dust, we would simply laugh at it. Here, unarguably, is a display of shoes and boots that aren't made for walking in, unless by "walking" you mean covering the few yards from taxi to nightclub door. No, these are shoes designed with another function in mind – at once objectifying the female form, and, bizarrely, by adding impressive inches to the wearer's height, making her feel "empowered" (even if she is hobbled). Louboutins, it could be argued, are the crotchless knickers of the shoe world: devoid of practical function but loaded with aggressive-submissive intent.

Making an event of displaying Louboutin's "personal archive" is a bit of a challenge, too. The Design Museum has gone for moody lighting, cabaret music and mirrored shelving, upmarket shoe-shop style, which has the effect of exaggerating still further the heights of the heels, some of which are so thin, so long, and so metallic, they could double as radio aerials. The mirrors also draw attention to Louboutin's signature red sole, which the designer recently tried (unsuccessfully) to stop anyone else using. You can see why he thought it worth going to court: a flash of that sole is a saucy exclamation mark, a suggestion of a lascivious tongue. It's all of a piece.

The designs are indeed imaginative in terms of decoration and global reference. Thigh-high snakeskin boots have been "tagged" in fluorescent spray-paint by a New York graffiti artist. Another pair in black suede are fringed from thigh to toe like a woolly poodle. A knee-boot sheathes the leg in what resembles lace tights – a nice conceit. A court shoe "inspired by the figure of Marlene Dietrich" comes in flesh-coloured mousseline appliquéd with licks of diamante flames: nudity and bling in a single shapely package.

The museum is oddly sparing with information. It would be good to know how many copies are made of each design. And was the range "inspired by Tina Turner" made for the singer to wear? If so, why no evidence of the items in use? Tellingly, the only designs shown adorning feet are in a section called "Fetish", featuring photographs by David Lynch. Here, naked models sprawl across furnishings – surely because they are unable to stand, such is the footwear's bizarre construction, heels running parallel to sole or curved like a parrot's beak.

It's often been observed that desire defies sense and reason. These, then, qualify as true objects of desire.

To 9 July (020-7940 8790)