Undoubtedly, it's the grandest social gathering you will be invited to this autumn. Emperors, popes and princes; doges, duchesses and diplomats will all be attending. Add a handful of clerics and scholars, a few old bankers and new brides, the occasional poet and the odd courtesan to the list, throw in a few gatecrashers whom nobody recognises, and you can be pretty sure that the National Gallery's latest party will be a lively mix.

Here you can meet anyone from the demure debutante to the overdressed drama queen, from the emperor who decided to come dressed as a basket of vegetables to the artist who insists on discussing his medical problems (he is worried apparently that he has syphilis). Here is the shabby old man who forgot to shave before coming. There is the stout Lady Dacre with her long bad-luck tale. Here is the serene young beauty who blushes as she tells you about her betrothal, there is the hideous old dowager with her wrinkled bosoms pushed out like a pair of deflating balloons.

Renaissance Faces is a vivacious and varied exhibition that has the slightly extemporary feel of a party that, if at first it intended to be snootily exclusive, quickly gave up when certain grandees (Leonardo, for instance) turned down their invitations. A host of heterogeneous substitutes were asked instead. Still, several of the most celebrated inhabitants of the National Gallery seem to have considered it worth coming. Something like a third of the paintings on display are drawn from the collection's rich holdings in century culture was becoming more interested in the notion of individual identity. Portraiture accordingly became increasingly complex. Now, it had to present a physical likeness, capture conventions of behaviour as defined by age and gender, beauty or class, represent spiritual qualities and evoke a sense of character and emotional response to boot. This presented great challenges to the artist's technical ingenuity and his empathetic insight.

This show follows a vaguely chronological progress that, though it hops about all over the place in the middle, leads the spectator from the strict stylisation of a precise little profile c1400 to the painterly bravado of mid-16th century Titian, who captures his subjects with psychological acuity and sensual panache.

In between it makes sense of what feels like a bit of a clutter - there are paintings and marbles and medallions and bronzes, drawings, woodcuts and coins - by sorting them out into loosely thematic galleries: “courtship and friendship”, “family” and “love and beauty”, for example. Here are portraits to mark every moment from pregnancy to death: portraits that serve as proof of power, as marks of status, as signs of love, as reminders of mortality, as demonstrations of skill. But it's all rather arbitrary and you end up with oddly heterogeneous galleries. The “identity, attributes, allegory” room, for instance, which puts a pair of grand ambassadors in conversation with a greedy art collector, a woman who likes spinning and a mad visionary monk, starts to feel a bit like the kitchen at a party. No one has much in common except the glass of wine they are clutching.

Currents of wider argument, however, carry this show along. The visitor can watch painting establishing its precedence, for instance. Sculpture, of course, must have seemed enviably literal - and not least as far as the Strozzi family were concerned. What better way could they have found to demonstrate the solidity of their business than by capturing the corpulent likeness of one of their most prominent members in a solid block of marble? But slowly the painter learns to rival a three-dimensional medium. Bellini celebrates the magic of oil pigment in his marvellous portrait of Doge Loredan. The serenely impassive potentate poses behind his stone parapet like some classical bust. But is that a smile that plays about the sitter's thin lips? The statue comes to life.

Painters experiment with ways of mimicking reality, ranging from the meticulous rendition of every minute detail through the development of dramatic “action” poses to the first use of expressionistic brushwork. And in an era in which artists travelled widely and fashions shifted quickly, this exhibition importantly does not make distinctions between north and south but, emphasising the cross-fertilisation of ideas, shuffles up the pictures. Here are Florentine painters experimenting with typically Dutch-style landscape backgrounds or Botticelli turning away from the traditional serene profile to the more lifelike Flemish three-quarter view but then taking it one radical step farther and presenting a young man head-on, which, though in our age of endless photographic reproductions it may be hard to remember, must have been breathtakingly striking at the time.

And yet, for all that it traces broad art-historical developments, for all that its catalogue essays encourage us to explore relationships between patrons, artists and sitters, the processes of making or underpinning notions of beauty and spiritual belief, this exhibition feels curiously unfocused.

It has some great moments. Jan van Eyck and his wife are reunited for the first time in about three centuries. The magnificently ugly old woman (on whom John Tenniel famously based the Duchess in his Alice in Wonderland illustrations) finds a companion for the first time since about 1645. A grandfather is brought back to life by Ghirlandaio, who, having sketched him as a corpse, resurrects him again in an enchantingly tender double portrait in which his little curly-haired grandson (maybe not even born at the time of his death) nestles up to his chest.

The show reaches a grand finale as Antonis Mor and Titian compete, their paintings ranked up on either side of the gallery as they once were in the time of their patron Philip II, when spectators (who at that time would have had to be taught how to look at Titian from a distance) gathered to argue the relative merits of Mor's literal accuracy (so psychologically evocative in the case of the court buffoon and, when it comes to Philip, far less flattering than Titian: he makes him look like a thug) and Titian's expressive brushwork.

But there are low points too - sometimes quite literally in the “portraits of rulers” gallery, where canvases and sculptures that were meant to look down disdainfully are brought down to our humble level, or when Raphael and Titian's popes are hung side by side. Two portraits, both magnificent individually, drain the energy from one another.

Perhaps it is best to think of this show less as a coherent study than simply as a delightful gathering of people whom we are now offered the opportunity to meet. Enjoy a series of vivid encounters with historical faces. Can you see the future cruelty in the giggling features of a little Henry VIII? Do you recognise the moping languor of Hilliard's young courtier crossed in love? You could almost pick the fallen hair from that old man's shoulder. Notice the shy way that the fingers of those newlyweds tangle. Imagine how fragile that child must have felt to his father in an age when infant mortality snatched your heir away so easily.

We circulate through the crowd, and then we leave. Probably, as with most parties, there was no particular point. But maybe a couple of the people you met made a lasting impression; maybe they charmed, instructed, interested or moved. The rest of the experience is probably a happy blur of fun.

Renaissance Faces: Van Eyck to Titian is at the National Gallery, WC2 (020-7747 2885; www.nationalgallery.org), from tomorrow

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