Ask someone to free-associate with the word “Byzantine” and you will hear of a devious cast of mind, convoluted bureaucracy and domed buildings. With a little more knowledge, the list might extend to Greek fire, eunuchs, chariot racing, inventing the fork, the worship of icons, pictorial mosaics and heights of design and artifice in hammered gold and gold enamelling.

The Icon of the Heavenly Ladder of St John Klimakos, originally from Constantinople or Sinai, painted in the late 12th century

Not all of these are touched on in the Royal Academy’s new survey of Byzantine art and craft, but the last three are there in sumptuous quantity. There are, too, many artworks and artefacts (among more than 300 on display) that we less often associate with the workshops of Constantinople and its 1,000 year empire: exquisitely carved ivories, bejewelled book covers, brilliant silverwork, elegant calligraphy and embroidery and the silver spoons, plates and brightly painted ceramics of domestic life.

The exhibition’s first intention is to show the broad ambition and intricate skill of Byzantine design, mostly in small objects, and at the same time to demonstrate how religious and political ideas permeated everyday life in the empire. The ivories from the 5th century (some of the oldest things in the show) are particularly striking. Several are luxury domestic objects, such as two combs, fine-toothed enough to cope with many an outbreak of nits, but with more high-minded relief sculpture in their solid sections – one showing mythological sea creatures and the other with personifications of Rome and Constantinople, one on each side. When this comb was made in Byzantine Egypt, propaganda saw Byzantium as the flip-side of Rome, one of the two political faces of the known world. Rome may have been then in decline, and Byzantium in the ascendant, but the older capital’s prestige remained as an essential reference point for its sister’s growing wealth and status.

More overtly political ivories make the same point. These are carved diptychs (paired panels, hinged to stand upright) regularly issued in Constantinople and Rome to mark the appointment of consuls. The consuls served for a year and their job was to arrange public entertainments, though this did not diminish them since ceremony and games were at the heart of imperial politics, and vice versa. In these diptychs the newly appointed consul is generally seen enthroned, with personifications of both great imperial cities supporting him, one on each side, while below is a representation of his duties – a stadium stag hunt (clearly showing parallels with modern bull-fighting), a chariot race, or slaves pouring out sacks full of coins to make a consular handout to the Hippodrome crowd.

If races and games coincided with politics, so did religion. Byzantium was raised to the status of a capital by the same emperor who made the Mediterranean Christian. Having lost count of the number of Annunciations I saw in this show across various media, it seemed possible that the Byzantines’ fondness for this subject (which is no less than the conception of Christianity) is linked to Constantine I’s conception and nurturing of the new Christian empire. At all events, Christianity permeated Byzantine life and its artefacts. The last rooms in this exhibition are devoted to the most sacred of all these, the icons, which in modern eyes are the most recognisable of all Byzantine objects.

The Antioch Chalice, made of silver and silver-gilt in Syria, 6th century

Today the word “iconic” is draped over anything we regard as special, but icons themselves were not special in the way people may now think of a Rolling Stones album cover, or Damien Hirst’s pickled shark. Nor were they simply works of art, but comparable to sacred relics in the medieval west: objects invested with the identity of God or of the saint portrayed. Any pious person who tried hard enough, it was thought, could establish a hotline to the divine through the painting. The Virgin Psychosostria (Saviour of Souls) is the most mystically powerful of the icons to be seen here. It is based on a famous icon kept in Constantinople, which was believed to have been painted by the apostle Luke, and to be miracle-working. This power was considered transferable, by God’s creative power working through the artist, from the original to the copy. Such icons have an aura that is almost impossible to experience in a museum context, and one is left considering them “merely” as paintings. As such, they are not crowd-pleasingly beautiful, but that is not the standard by which to judge them.

In Byzantium, the Christian God even took over the work of Mammon. The show has a large display of gold and silver coins issued throughout the history of the empire, from 335, when Constantine I still ruled, until 1453, when the Ottoman Turks finally overwhelmed the capital and destroyed its civilisation. These coins show just how carefully a Byzantine ruler managed his image. This was not just money, but an assertion of power that travelled to every part of the empire and beyond, to impress foreigners from Britain to India, and from the Russian steppes to the edge of equatorial Africa. It was Justinian the Great, in the 6th century, who first rejected the coins’ traditional profile portrait; thereafter the gold solidus always showed emperors and empresses boldly confronting their people face-on, as if to demand obeisance. It was a century later that faith was introduced into Byzantine economics when the obverse side of the coin began to display pictures of Christ, the virgin, a powerful saint, or the cross. Thus was the imperial bank backed by divine guarantees.

It was, in fact, a highly resilient currency, comparable in more recent history to the British pound or American dollar at their height. The difference is the Byzantine currency’s durability. The solidus maintained a rocklike stability for 700 years, until the 11th century, when the increasingly beleaguered Byzantine mints were forced to debase the gold standard with increasing increments of silver.

The last of these debased coins in the Academy’s numismatic display case has special poignancy. It was minted under siege conditions by the last emperor, Constantine XI, in the spring of 1453, to pay the last remaining western mercenaries defending the city against the Ottoman Turks. Within days Turkish cannon had battered down the great walls, the population was massacred and the churches and treasuries looted. Since the finest things were concentrated in the capital, far richer and more precious objects were stored within the city than are seen in this exhibition. But the Ottomans proceeded to drape their horses and dogs with the patriarchal robes, make bonfires of books and icons and eat and drink looted food from the sacred vessels.

The empire had shrunk by this time to the size of a mini-state, but in its mind and habits it was still imperial. It can be said that no empire has ever fallen so decisively, and with such loss. This is a big show, but it gives only a taste of that loss. It feels at times, too, like a slightly academic exercise, and some visitors will wish there was more local colour – the smell of the spice markets, the scorch of Greek fire. But I would defy anyone not to relish the brilliant things, those made by the icon-painters and “the golden smithies of the Emperor”.

‘Byzantium 330-1453’, Royal Academy of Arts, London, until 22 March 2009. Tel: +44 020 7300 8000