The four corners of the gallery show specifically religious art, including a whole carved wooden minbar, or pulpit; art from the Safavids of 16th century Iran whose reign marked a flowering in the art of ceramics; Ottaman art, and a general introduction to the beginnings of Islam.

Curator Tim Stanley explained that the gallery shows not just the art of Islam as a religion, but as a political force. By 750 the Islamic empire stretched from Spain and Morocco in the West to the banks of the Indus in what is now Pakistan. The influence of Islamic style therefore embraces a large number of places and cultures. The V&A has one of the best collections of Islamic art in a museum, because its curators have been passionate about the subject since the founding of the museum. Back in 1850 Owen Jones probably knew more about Islamic Art than any other Westerner, and used a founding lecture to put forward the idea that Islamic decorative art was the best in the world: because its non-illusionist flat patterns fitted function to form.

Therefore William Morris's famous advice to "have nothing in your houses that you do not know to be useful, or believe to be beautiful" nicely fits many of the objects shown here, which are both lovely and functional. Indeed Morris' own art was strongly influenced by Islamic art. It was on his advice that the V&A obtained the 'star' piece in its collection, the Ardabil carpet. The carpet reached Britain in the 1880s, sold off by the shrine where it lived for three centuries, to pay for repairs.

Though there are older carpets on show in the gallery, it is the earliest one with a date: 946 which is equivalent to 1539 - 40 in the Western calendar. It is remarkable for the technical skill involved in putting together such a vast object as a single piece. Some visitors may feel more attracted to the reds of the Ottoman carpets, or flower patterns of the carpet which belonged to William Morris himself for many years, but it has a vital place in the history of design.

The exhibition also demonstrates that, sitting at the heart of the 'old world' the Islamic states did not form a closed society, but were open to influence from the cultures around them. So the Chinese genius for ceramics was first copied for the tables of the great and fashionable, and then gradually transformed into new ceramic designs that we now recognise as traditionally Islamic.

Meanwhile in the West, the Islamic empire was a force to be fought and feared, yet art from Islamic countries was extremely popular, even in the Medieval period. We see metal trays and vessels intricately decorated with Muslim designs that reached the West. Some Medieval Western craftsmen made objects with Islamic designs to feed the fashion. So the arts of the Islamic world were familiar in Britain for many centuries before significant numbers of Muslims had ever visited this country.

For fans of design, this is a beautiful exhibition, showing some of the archetypes of the carpet, ceramic, tile and calligraphic design that are now very familiar. However, the histories and personalities sitting behind these objects remain more elusive.

There are two stories of dramatic reversals of fortune. Three kaftans are shown that were placed in the graves of children. These may have been three of the 19 sons of Sultan Murat III who were all executed at the same time on the accession of their half brother Mehmet III - a terrible measure to prevent dynastic wars. It was a solution that was never repeated.

Elsewhere we hear about Qa'itbay who first enters history when he was brought to Egypt as a slave. He became known as a brilliant military commander and ended his life as a powerful Sultan - ruling from 1468 for 28 years.

But largely the focus of the exhibition is on the art, and its longlasting influence. Mehmet the Conqueror commissioned patterns for Ottoman carpets between 1451 - 81 that remained in commercial production for centuries, and were meticulously reproduced in paint by Italian Renaissance painters, and also by Hans Holbein. So as well as being a history of art, it casts interesting light on how ideas last and spread between cultures. Next door in the Science Museum the Non-Western medicine galleries show a similar transfer of scientific thought from East to West

Despite the introduction of some low key interactives like videos and listening posts this is very much an exhibition for informed adults rather than children. However three weekends of Middle Eastern culture at the V&A are likely to have much broader appeal - the first being Tulips, Tiles and Coffee Culture - a Turkish weekend on the 5th and 6th August. There will be food, dancing and dressing up as well as more serious lectures.

London now has two landmark galleries demonstrating the art of the Islamic world: the V&A's Jameel Gallery and the British Museum's John Addis Gallery of Islamic Art. Both give an excellent introduction to the innovation and skills of Muslim artists. What it would be nice to see now from London museums is a complementary social history - explaining to us what life was like for the Sultans, the poets, the soldiers, the craftsmen, the women, whose life stories still escape us as we look at these beautiful things.