Here’s a handy, clear summary of the Neoclassical period in European art and literature from Imaginative Literature II: from Cervantes to Dostoevsky, a Supplement to Encyclopedia Brittanica’s Great Books of the Western World set, by Mortimer J. Adler and Seymour Cain:
Neoclassicism, which arose in France in the seventeenth century, aimed to imitate the clarity and simplicity of the ancient Greek and Latin classics. It sought a literature in which decorum and correctness according to fixed rules prevailed. Inspired by the rationalism of the new science and philosophy of the age (Newton, Descartes, etc.), it emphasized intellectual perfection — the witty thought pefectly expressed in an elegant phrase — rather than imaginative color or feeling. In form, Neoclassicism fostered formally correct, elegant, urbane expression. In thought, it emphasized an unsentimental realism, which viewed certain characteristics of human nature as permanent and univeral, and did not consider the individual variations important or interesting. (The French Neoclassical tragedians put the ancient Greeks into seventeenth-century French clothing.)
The great Neoclassical literature was that of the French writers of the seventeenth century — Moliere, Racine, Corneille, La Fontaine, etc. — and their influence extended to the latter half of the eighteenth century and was represented by Alexander Pope, Addison and Steele, Samuel Johnson, and other writers of the so-called Augustan Age of English letters. It was in England that the reaction against Neoclassicism, called Romanticism, originated among such poets as James Thomson, Thomas Gray, William Cowper, Robert Burns, and William Blake. From England the revolt spread to France, Germany, and Italy. The French philosopher Jean Jacques Rousseau was the greatest single intellectual influence on the Romantic movement. (106-107)
Adler and Cain are equally lucid at portraying the shift from Neoclassical to Romantic:
The Romantics espoused imagination, feeling, passion, vitality, nature, and individuality, as against the decorum, rules and universality, of the Neoclassicists. The Romantics emphasized the inner depths of the human soul and the immensities of the natural world, the expression of intimate personal experience, of joy, and especially of melancholy and suffering. For the Neoclassicists the dominating attitude was rational detachment; for the Romantics it was sensitive inolvement. The Neoclassicists stressed the values and forms of European civilization and urban, advanced, Western society. The Romantics stressed the natural, the primitive, the medieval, the oriental, the ancient, and remote. (107)
While fundamental periodization of this kind is unstable, slippery, and far from absolute, such provisional distinctions are practical, sensible ways to grasp the intellectual impulses happening in the 18th century.