In Europe, neoclassicism began as a reaction against the Baroque and Rococo styles, and a desired return to the art of Romanesque and Renaissance classicism. Each individual grouping of Neoclassicism, whether affecting architecture or the visual arts, has attempted to capture the ideas of times gone by to utilize them in forms of art that were considered modern at the time. In neoclassicist painting in particular, the subject matter seems to hearken back to those classical ideas by reviving those Greek to Renaissance themes, and forcing them into peculiar constraints that would recreate the elements into new formats.
The Neoclassical style of artwork was heavily present during both the American and French Revolutions, and revival in the interest of classical thought in the style of ancient Greece and Rome, at times affecting a more Byzantine stance in some countries. A counterbalance came in the form of the Romanticism movement, and it never replaced Neoclassicism so much as aided in the influencing of many artists throughout the 19th century and beyond. When the architecture began to dominate the main aspects of neoclassicism, and has been found to be academically selective of the best Roman models guided with self-restraint.
At first, the style had been grafted with other popular European forms of architecture, and this style became quite pronounced as neo-classically inspired furnishings were popular for the time. The style soon had international renown, and it was at this point that the architecture became strongly influenced by Roman designs after the discoveries at Pompeii, during excavations that took place at that time. Though all these designs seem a bit absurd and overcomplicated nowadays, there was a flush of Greek inspired work in the forms of busts and vases after 1800, and this was called the Greek revival.
Continuing to be a force after the turn of the 19th century, even as Romanticism and Gothic styles took favor, but it seemed anti-modern to influential critical circles by the late 19th century. In the mid-19th century, several European cities had grandiose examples of the neoclassical style of architecture, and even early American architecture reflected this movement in various national monuments, and some of those monuments were the Lincoln Memorial and the National Gallery in Washington D. C. Soon, however, World War II would shatter those preconceptions for the world round.
Covertly, there were many modernists that chose to express a neoclassical influence with subtle tribute here and there, and even Picasso played around with reincorporating neoclassical motifs into his work at one time. Even the Art Deco style was using these ideas on a very sly level of utilization, playing with classic Grecian lines and even breaking out in American culture through architecture and the dime by 1950, and became a strong ideology in the time between both World Wars. This literary and very literal side of the movement rejected the romanticism of Dada, for example, for the restraint of religion and reactionary politics.
It can be a difficult bout to sort through all these items to find the ideal artwork that you would enjoy, and there many whose catalogs are extensive to say the least, making it quite an effort to glimpse through all of those works to find the pieces that you would enjoy the most. Finding the particular classifications that art periods fall under, such as neoclassicism, can keep your interest guided by where you can find most amount of work that you can acquire. Keep in mind, however, that many of these pieces are quite priceless to many collectors, and that buying a print of a particular famed work mat be more cost-effective for your budget.