It's so easy to see the point of a painting by Peter Doig. You don't have to clamber about in a scaffolding of theory or worry about finding your place in art history or go leafing through long biographical notes. You just need to look. Its all there in the pictures: and not just in the subject matter, in the eerie landscapes with their mood of twilit enchantment, but in the way that they are painted too - with veil upon veil of seeping colour, with swags and smears and spatters of paint, with delicate washes and fat, spilt globules, with glistering lights and strange, lurid glows. It's perfectly simple to explain the pleasure. These paintings are pretty.

But don't get nervous. You are allowed to admit that you like them because Doig is postmodernist too. His images grow from accretions of references. These range from straightforward lifts to passing allusions. They can incorporate anything from old holiday photographs to art-historical quotations, from magazine images to childhood memories, from sporting scenes to Hollywood stills. Here, like some stray who has wandered into the wrong picture is Van Gogh's famous sower, and there is Doig's brother on the day the pond froze. Here is the canoe that drifts down the Friday the 13th river, and there is the Trinidadian whom Doig watched strangling a pelican. So, if you are one of those anoraks who likes your aesthetics to be inter-referential, you will be on safe ground.

No wonder Doig has been such a hit on the art scene. How often can “pretty” and “postmodern” be used in the same sentence? How often can the decorative also be cutting-edge? And how often can paintings that pinch so many styles - anything from pointillist tip-of-the brush touches to entire Gauguin patterns - remain so distinct in their look?

Little wonder that Doig's paintings fetch astonishing prices. When his White Canoe was put up for sale at auction last year, it sold for £5.7 million, making it the most expensive work yet by a living European painter. Private collectors compete for them because, however committed you are to the avant-garde, it's a lot easier to accommodate a landscape painting than a cut-up cow.

Doig was in his early thirties when he won the first of a series of accolades that rapidly led him to a 1994 Turner Prize nomination (though he did not win). Ever since, he has popped up all over the place. In an art world dominated by the conceptual antics of the Brit-pack, he was enthusiastically hailed as the great white hope of painting (with his close friend and now neighbour Chris Ofili as its black face).

But can a mid-career survey add anything to the picture? Tate Britain (firmly claiming Doig as British although, brought up from the age of two in Trinidad and spending his teens in Canada, he is probably more of a nomad than a national icon) clearly thinks so. The gallery, which owns a couple of his most alluring large canvases, now sets them in the context of some 40 loans scrabbled back from private collectors the world over.

The spectator can trace the roaming progression of Doig's development. Snowy Canadian expanses give way to the burnt ochres of Trinidad. The spinning psychedelic influences of youth mature into more meditative, vaporous moods. The endless layered accretions start to thin until the images are barely more than ghostly apparitions.

But to follow some sequential narrative is to miss the point and, more importantly, the pleasure of these works. In a film a succession of images follow one upon the other to tell a story. Doig's paintings are supposed to work in another way. Hundreds of images are overlaid, one on top of the next. You look down through their depths. It's a bit like watching a coin falling through deep, dark water. His images fall through layer upon layer of memory and half-memory, slowly coming to settle. You start with the prettily sparkling surface. But you are waiting to see what dark, bottom sediments will be stirred.

The eye takes you on a voyage of discovery. One moment what you are looking at is little more than a giant Christmas-card scene. The next you are almost blinking to keep the snowflakes out of your lashes. You peer closer. But you lose your grip on rational spaces. Your eye grows unfocused. The paint starts to float. Sometimes it feels almost repellent. It has a sour, sickly sheen. And perhaps you start drifting. You feel as if you are lost in some semi-detached dream world. But, as you wander away from the painting, the image swims slowly back to the surface. Except now it feels different. It may still look pretty, but you have felt the pull of its undertow.

The paintings in this show are thoughtfully hung so that the visitor can move from far-off vista to abrupt close up, from slantwise glance to full-frontal confrontation. You are encouraged to approach them from as many angles as possible. This is important. These are works that you need to experience.

But the only point of gathering so many together is to try to allow each visitor the opportunity to remain undisturbed with one picture (not least since photographic reproductions can't really convey a sense of how they work). You need a degree of space and solitude to enter Doig's eerie land of reflections. You need time for the processes of sensual experience to take place, for the feelings and emotions to distil. It is a pity that a few more of the most effective works - including White Canoe - have not been included.

The Tate should have included more “greatest hits”. Instead, putting an explanatory focus on his artistic development, it includes lots of pieces - rooms full of drawings, for instance, or later works that feel undigested - that add nothing to our appreciation. Like the dreams he evokes, Doig's visions disintegrate when they are analysed. The atmosphere dissolves. These pictures have a mysterious resonance, not a rational meaning. Just look at a couple and enjoy them because they are so pretty.

Peter Doig is at Tate Britain (020-7887 8888) until April 27

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