I'm reading the Aeneid (Fagles translation), and I see references to Europe and Asia. I don't know if it's just the translation, but it made me wonder when this thing called "Europe" and "Asia" came to be. Who made the distinction? How was the distinction enforced? Where were the boundaries in ancient times? (I'm guessing Greeks/Romans are the culprits here, but I suppose that's why I'm asking...I know the Europa myth, but how did that name become the name of a [sub]continent*) *I learned that Europe and Asia were separate continents in school, but my husband was raised in a Soviet country, and always insisted that there was one continent, Eurasia.
I can speak to the Europe part of your question,
'Europe' exists in the classical imagination, but not in the sense of being a separate area, but rather part of a unified Mediterranean world comprising Africa, Asia (Minor) and Europe.
That conception of the world survived well into late antiquity, even after the establishment of the barbarian kingdoms in the old Western Empire. Even with the breakdown in trade and communication, there is still a fundamental conception of a united world, centred around fighting over the old Roman legacy (which is why you get Theodoric et al laying claim to Roman symbols), in which the Eastern emperors were first among equals.
This only ends with the Arab invasion. The domination of North Africa and much of 'known' Asia by the Arabs lends geography a new meaning for westerners in which Christianity is crucial. It is around 800 AD that 'Christendom' is invented, to give spatial shape to those areas opposing the Islamic 'Other'. The first time Christendom and Europe are mentioned in tandem is regarding the victory at Poitiers. Christianity thus sharpened the modern geographic conception of Europe.
Since then, Christendom gets fought over, and a sequence of schism and ruthless exclusion of the loser leads to a narrower and narrower concept that increasingly doesn't match with the intellectual community of Europe. This comes to a head in the Reformation, where it is simply no longer feasable to exclude Luther et al from 'Christendom', because they are engaged in dialogue with other inellectuals across the sectarian divide, i.e. they are part of the same community. So 'Europe' becomes the primary signifier for the geographic areas of this community, as a concept which allows for diversity.
From 1500-1800, powers aiming at hegemony in Europe always invoked the old united Christendom, while the balancing coalitions opposing them invoke 'Europe' as an inherently diverse community. After Westphalia, Europe is seen as the geographic arena for a balance of power system, and the last time Christendom is mentioned is in the Treaty of Utrecht,
Everyone playing a role in the balance in this period gets a lasting identity as European, while those on the fringes are 'sort' of accepted as such i.e. Turkey and Russia intermitently played balancing roles. This era overlaps with the Rennaissance and more importantly the Enlightenment, which inject a civilisatory discourse into the European identity - those n the inside are superior, and those on the edges less so. This is when you get a construction of West vs a less civilised Eastern Europe by people like Voltaire, which Russians desperately opposed e.g. Peter forced his court to ape the French court, and installed a completely arbitrary fence in an enormous plain marking the edge of Europe.
Nobody in the West really takes this seriously, and after the French Revolution, Europe becomes seen as a harbinger for a set of universal values - liberty, equality, etc,, which only further contrast and orientalise Russia and Turkey as being in the same boat as the extra-European world.
This gets contested in the late 1800s by the Romantics, who see Europe as more than just primus inter paribus, but as ''special' , and certian peoples as more special than others. Europe in this era becomes less important, and nations within Europe become more so, and Russians like Dostoyevsky emphasise Russia's Eurasian character, birthing Pan-Slavism. Added to Communism's supposed commitment to racial equality , this is what drives the Russian conception of geography, seeing Russia as a single entity spanning a single continent. There is also the parallel hurt feelings at being continuously excluded from a superior conception of Europe.
TL:DR - Europe has changed from a loose, unimportant word first into a geogrphic representation of spiritual borders, and later into an exclusionary concept denoting superiority.
This has actually been asked a number of times before
You might also check out The Myth of Continents.