I have decided not to put the following in my own words because I find the way that the scholars of the arts describe the movement far better than I ever can!
Neoclassical art, also known as Neoclassicism and Classicism.
The movement was widespread and was influential in painting and visual arts. The movement started in the 1760s, and would reach its height in the 1780s and ’90s, it would last until the 1840s and ’50s.
Paintings would take “the form of an emphasis on austere linear design in the depiction of Classical themes and subject matter, using archaeologically correct settings and clothing.”
The art of Neoclassicism “is an aesthetic attitude based on the art of Greece and Rome in antiquity, which invokes harmony, clarity, restraint, universality, and idealism. In the context of the tradition, Classicism refers either to the art produced in antiquity or to later art inspired by that of antiquity, while Neoclassicism always refers to the art produced later but inspired by antiquity.”
To Classicize the artists would “tend to prefer somewhat more specific qualities, which include line over colour, straight lines over curves, frontality and closed compositions over diagonal compositions into deep space, and the general over the particular.”
Neoclassicism grew in part due to its “reaction against the sensuous and frivolously decorative Rococo style that had dominated European art from the 1720s. But an even more profound stimulus was the new and more scientific interest in Classical antiquity that arose in the 18th century.”
Neoclassicism was influenced by “new archaeological discoveries, particularly the exploration and excavation of the buried Roman cities of Herculaneum and Pompeii (the excavations of which began in 1738 and 1748, respectively). And, from the second decade of the 18th century on, a number of influential publications by Bernard de Montfaucon, Giovanni Battista Piranesi, the comte de Caylus, and antiquarian Robert Wood provided engraved views of Roman monuments and other antiquities and further quickened interest in the Classical past.”
A new understanding was “distilled from these discoveries and publications in turn enabled European scholars for the first time to discern separate and distinct chronological periods in Greco-Roman art, and this new sense of a plurality of ancient styles replaced the older, unqualified veneration of Roman art and encouraged a dawning interest in purely Greek antiquities.”
A “German scholar Johann Joachim Winckelmann’s writings and sophisticated theorizings were especially influential in this regard. Winckelmann saw in Greek sculpture “a noble simplicity and quiet grandeur” and called for artists to imitate Greek art. He claimed that in doing so such artists would obtain idealized depictions of natural forms that had been stripped of all transitory and individualistic aspects, and their images would thus attain a universal and archetypal significance.”
Painting
Neoclassicism “in painting was initially not stylistically distinct from the French Rococo and other styles that had preceded it. This was partly because, whereas it was possible for architecture and sculpture to be modelled on prototypes in these media that had actually survived from Classical antiquity, those few Classical paintings that had survived were minor or merely ornamental works—until, that is, the discoveries made at Herculaneum and Pompeii.”
The earliest Neoclassical painters were:
Joseph-Marie Vien
These “artists were active during the 1750s, ’60s, and ’70s. Each of those painters, though they may have used poses and figural arrangements from ancient sculptures and vase paintings, was strongly influenced by preceding stylistic trends.”
A Neoclassical work such as Mengs’s Parnassus (1761) was an important work due to “much of its inspiration to 17th-century Classicism and to Raphael for both the poses of its figures and its general composition. Many of the early paintings of the Neoclassical artist Benjamin West derive their compositions from works by Nicolas Poussin, and Kauffmann’s sentimental subjects dressed in antique garb are basically Rococo in their softened, decorative prettiness. Mengs’s close association with Winckelmann led to his being influenced by the ideal beauty that the latter so ardently expounded, but the church and palace ceilings decorated by Mengs owe more to existing Italian Baroque traditions than to anything Greek or Roman.”


“A more rigorously Neoclassical painting style arose in France in the 1780s under the leadership of Jacques-Louis David. He and his contemporary Jean-François-Pierre Peyron were interested in narrative painting rather than the ideal grace that fascinated Mengs. Just before and during the French Revolution, these and other painters adopted stirring moral subject matter from Roman history and celebrated the values of simplicity, austerity, heroism, and stoic virtue that were traditionally associated with the Roman Republic, thus drawing parallels between that time and the contemporary struggle for liberty in France. David’s history paintings Oath of the Horatii (1784) and Lictors Bringing to Brutus the Bodies of His Sons (1789) display a gravity and decorum deriving from Classical tragedy, a certain rhetorical quality of gesture, and patterns of drapery influenced by ancient sculpture. To some extent these elements were anticipated by British and American artists such as Hamilton and West, but in David’s works the dramatic confrontations of the figures are starker and in clearer profile on the same plane, the setting is more monumental, and the diagonal compositional movements, large groupings of figures, and turbulent draperies of the Baroque have been almost entirely repudiated. This style was ruthlessly austere and uncompromising, and it is not surprising that it came to be associated with the French Revolution (in which David actively participated).”
“Neoclassicism as generally manifested in European painting by the 1790s emphasized the qualities of outline and linear design over those of colour, atmosphere, and effects of light. Widely disseminated engravings of Classical sculptures and Greek vase paintings helped determine that bias, which is clearly seen in the outline illustrations made by British sculptor John Flaxman in the 1790s for editions of the works of Homer, Aeschylus, and Dante. Those illustrations are notable for their drastic and powerful simplification of the human body, their denial of pictorial space, and their minimal stage setting. That austere linearity when depicting the human form was adopted by many other British figural artists, including the Swiss-born Henry Fuseli and William Blake.”

“Neoclassical painters attached great importance to depicting the costumes, settings, and details of their Classical subject matter with as much historical accuracy as possible. This worked well enough when illustrating an incident found in the pages of Homer, but it raised the question of whether a modern hero or famous person should be portrayed in Classical or contemporary dress. This issue was never satisfactorily resolved, except perhaps in David’s brilliantly evocative portraits of sitters wearing the then-fashionable antique garb, as in his Portrait of Madame Récamier (1800).”
British Painting

“Gavin Hamilton—Scottish painter, archaeologist, and dealer—spent most of his working life in Rome, and his paintings include two series of large and influential canvases of Homeric subjects. West and the Swiss-born Kauffmann were the most consistent exhibitors of history pieces in London during the 1760s. James Barry and Fuseli also were important. Blake, poet and painter, was a Neoclassicist to some extent.”
British Sculpture
“Prominent early British Neoclassical sculptors included John Wilton, Joseph Nollekens, John Bacon the Elder, John Deare, and Christopher Hewetson—the last two working mostly in Rome. The leading artist of the younger generation was John Flaxman, professor of sculpture at the Royal Academy and one of the few British artists of the period with an international reputation. The last generation of Neoclassicists included the sculptors Sir Richard Westmacott, John Bacon the Younger, Sir Francis Chantrey, Edward Hodges Baily, John Gibson, and William Behnes.”
Online Source: https://www.britannica.com/art/Neoclassicism