LONDON — During his lifetime, the Roman painter Pompeo Batoni was among the most celebrated artists in Europe, counting several popes among his patrons as well as Frederick the Great and Catherine of Russia. But only two years after his death in 1787, Sir Joshua Reynolds predicted that Batoni’s name would quickly fall into oblivion — and he was absolutely right.

Throughout the 19th and for most of the 20th century few artists were more completely forgotten — or, if remembered, more thoroughly despised. When the National Gallery of Wales bought one of his most impressive group portraits in 1947, it paid $388 — and that was mostly for the frame.

But, as with Reynolds, Batoni began to be rediscovered in the late 20th century, and is now having a sort of apotheosis in the form of a major exhibition at the National Gallery.

Born in Lucca in 1708 and trained as a goldsmith, Batoni went to Rome at the age of 19 and was soon supporting himself and his young family by flogging drawings of antique objects and statuary to British tourists. This early experience is worth emphasizing because he was to become one of the most incisive draftsmen of the 18th century, and because drawing played a crucial role in his creative process.

We still don’t know how or with whom he learned to paint, but even in his earliest paintings his technique is faultless and he is completely himself. As you walk through this show, you’ll see that the meticulously rendered details and vibrant colors you find at the beginning are still present at the end, and that most of the pictures are in pristine condition, having suffered hardly at all over the centuries.

His first commission in 1733 was for “The Vision of Saint Philip Neri,” which hangs in the first gallery. In some ways, it is a typical late Baroque altarpiece inspired by the 17th-century Bolognese painter Guido Reni’s treatment of the same subject. But look again and you notice the startling immediacy of the saint’s face, which is animated by the visionary intensity of his faith.

Then too, the Christ child is so lifelike, it must have been drawn from a real infant. As the aged saint kneels in devotion before the divine apparition, baby Jesus has only one job to do — hold the long-stemmed lily gracefully in his hand. But, appropriately for a saint who was famous for his sense of humor, things are going badly wrong, because the stem of the flower has drooped alarmingly and will soon bop St. Philip on the head. It is this kind of detail that makes Batoni inimitable. As we see in his mythological and allegorical paintings, Batoni was very much of his own time in believing that all the other arts seek inspiration in the written word, and also in his assumption that his patrons would instantly recognize the classical texts and visual quotations he used in pictures such as the “Death of Meleager” and “The Marriage of Cupid and Psyche.”

The rhetorical language of gesture and expression Batoni employs in these paintings is precisely what made them so unpopular with succeeding generations. But sophisticated contemporaries would have seen that here, and in allegorical figures representing “Purity of Heart” and “Meekness,” Batoni was taking the perfection of Raphael, Reni, and Domenicino to new heights of refinement.

Nowadays, what is instantly appealing to us about these pictures is their overwhelming sensuality. To paint nude and semi-nude figures, Batoni followed academic practice by first drawing detailed studies from the live model, then squaring the drawings for transfer to canvas.

Unusually, however, he continued to work from the living model while he was painting. This accounts for the tangible physicality of his figures and for the way each one, though drawn and modeled individually, is seamlessly integrated into the composition as a whole.

By 1750, Batoni was a well-established painter of religious and mythological pictures. But over the next decade, commissions for portraits of Irish and British visitors to Rome increased, until by the 1760s portraiture was the principal source of his considerable income.

Most of Batoni’s British sitters were young men in their 20s on the Grand Tour who, in terms of their wealth, and social and political connections, not only governed but owned most of this country. While it is true that some, such as the Duke of Gordon, could not have cared less about classical art and ancient history, others were buying the antique statues, and Renaissance and Baroque paintings, that today fill our museums or hang in great country houses. Some sitters are shown with one hand extended outward with the palm opened, in a gesture borrowed from Titian, while others cross their legs casually, as they do in portraits by van Dyck. Usually Batoni adds an antique statue to locate the setting of the portrait in Rome.

But the reason these pictures are so much more effective than those of any of his contemporaries is the way Batoni seizes on the details of his sitters’ clothing to create visual interest. In his portrait of Frederick, Lord North, for example, he deflects the viewer’s attention away from the goggle eyes and blubbery lips of the hideous nobleman by drawing our eye to his green frock coat with its rose red lapels and cuffs, worn over a lemon yellow waistcoat and enlivened by the long black ribbon tied loosely around the sitter’s throat.

Elsewhere, he rises to the challenge of rendering shot silks, lace ruffles, or the fur trim on a velvet dressing gown with as much care as he delineates the face.

Though I am utterly smitten with Batoni’s grand, full-length portraits, I can see why they might put some people off. Colonel the Honorable William Gordon, for example, wearing a kilt and swathing himself in a tartan cloak so long it trails on the ground, strikes a distinctly martial pose. With a huge broadsword in one hand and raising one foot to the base of an ancient statue, he looks as though he has come to Rome not to see the city but to sack it.

Though some of the history paintings are outright failures (“Prometheus Fashioning Man from Clay”) and Batoni could at times be insipid (“Diana and Cupid”), for the most part this show delivers the goods, culminating in two sublime and rarely seen masterpieces, the late altarpiece showing the marriage of saint Catherine with Saints Jerome and Lucy, and a full-length swagger portrait of the Roman senator Prince Abbondio Rezzonico enveloped from head to toe in scarlet robes of state.

This hugely enjoyable exhibition was organized by Edgar Peters Bowron and Peter Bjorn Kerber, who also wrote the lively catalog.

Until May 18, Trafalgar Square, www.nationalgallery.org.uk.