Classical antiquity is a broad and perhaps misleading term for a long period of European history, that begins roughly with the earliest recorded Greek poetry of Homer, and continues through the rise of Christianity and the fall of the Western Roman Empire.
Such a wide sampling of history and territory covers many rather disparate cultures and periods. "Classical antiquity" typically refers to an idealized vision of later people, of what was, in Lord Byron's words,
Western Europe than it is today. Respect for the "ancients" of Greece and Rome affected politics, philosophy, sculpture, literature, theatre, education, and even architecture.
In politics, the presence of a Roman Emperor was felt to be desirable long after the empire fell. This tendency reached its peak when Charlemagne was crowned "Roman Emperor" in the year 800, an act which led to the formation of the Holy Roman Empire. The notion that an emperor is a monarch who outranks a mere king dates from this period. In this political ideal, there would always be a Roman Empire, a state whose jurisdiction extended to the entire civilised world.
Epic poetry in Latin continued to be written and circulated well into the nineteenth century. John Milton and even Arthur Rimbaud got their first poetic educations in Latin. Genres like epic poetry, pastoral verse, and the endless use of characters and themes from Greek mythology left a deep mark on Western literature.
In architecture, there have been several Greek Revivals, which seem more inspired in retrospect by Roman architecture than Greek. Still, one needs only to look at Washington, DC to see a city filled with large marble buildings with façades made out to look like Roman temples, with columns constructed in the classical orders of architecture.
In philosophy, the efforts of St Thomas Aquinas were derived largely from the thought of Aristotle, despite the intervening change in religion from paganism to Christianity. Greek and Roman authorities such as Hippocrates and Galen formed the foundation of the practice of medicine even longer than Greek thought prevailed in philosophy. In the French theatre, tragedians such as Molière and Racine wrote plays on mythological or classical historical subjects and subjected them to the strict rules of the Three Unities derived from a remark by Aristotle. The desire to dance like a latter-day vision of how the ancient Greeks did it moved Isadora Duncan to create her brand of ballet.
"Classical antiquity," then, is the contemporary vision of Greek and Roman culture by their admirers from the more recent past. It remains a vision that many people in the twenty-first century continue to find compelling.
Articles that discuss various aspects of classical antiquity include: