However you regard the 'morality' of Empire, there is no disguising that in the states that succeeded Alexander the Great's Empire Greeks and Macedonians were on top. Not only were the Kings (and often Queens) of the Hellenistic States Macedonian or Greek, not only were the military backbone of these states landed Macedonian soldiers either settled by Alexander or brought over from Macedon, but even the urban control of many places were dominated by Greeks. When Alexander created the cities he personally created, he settled them with either Macedonian veterans, or a combination of Macedonians and locals. He only used Greeks once, as a last resort, as he didn't trust Greeks (there were political reasons not to, but I won't go into that here). But when the Seleucid Empire took control of the Asian portion of Alexander's Empire, it embarked upon a massive urbanisation program. Dozens of towns and cities were founded across the Empire, and many of these cities were planted with Greek settlers, and not just Macedonians. Also, unlike Alexander who exclusively founded cities on previously occupied sites, many of the Seleucid-founded cities were on completely new territory.

With that background out of the way, you can see how Greek-speaking populations were introduced to areas like India, Bactria, Mesopotamia and Afghanistan. It was not a case of ethnic cleansing or forced evictions, because the Seleucids were a Greek speaking elite now cut off from Greece and Macedon (Macedon had remained independent in the wake of the Wars of Succession after Alexander's death, and Greece had been in rebellion while Alexander was still alive) and actually required the co-operation of the local populations in order to actually function as a state.

There is actually a theory that Greeks were in Bactria before Alexander, as apparently Greek criminals were sent to Bactria by the Achaemenid Persians. Whatever the truth of the matter, in 250 BC Bactria was rich, powerful, and densely settled. In fact, it was already rich and densely settled, it had a canal-based irrigation system from the Bronze Age onwards and in the 1st Century BCE Zhang Qian estimated the area (known as Daxia to them) as having a million inhabitants. It was so rich and potent that around 250 BC it broke away from the Seleucid Empire. The Seleucids did attempt to take the area back, but gave up, and Bactria prospered. Greeks remained the ruling class of the Kingdom, but it is clear that local co-operation between Greeks and Bactrians (and the other cultures the Kingdom began to absorb) was fairly high, particularly when domestic industries still seem to have been dominated by the Bactrians. It is probably fair to say that by 180 BC, the Greeks of Bactria were probably all at least a quarter Bactrian themselves, and had adopted some interesting new practices such as Buddhism, but they still strongly asserted their Greekness. I will return to Bactria in a bit, but I need to move onto India and Afghanistan to make sense of the next part.

The Indian territories of the Seleucid Empire had very quickly been attacked by an emerging figure in India, the young Chandragupta Maurya. Overrunning this territory, he then signed a treaty with Seleukos essentially giving him the whole eastern half of Arachosia in return for a lot of war elephants (and possibly a dynastic marriage). This meant that the Greek communities in India and Arachosia were now themselves under foreign occupation, but they continued to thrive; Ashoka's Edicts were in some areas translated to Greek and Aramaic. The Greeks were certainly known in India by this point, they were reputed as being unusual as only having masters and slaves, and no further caste distinctions (this is clearly not entirely true but is interesting nonetheless), and also for not really having a tradition of asceticism. Ashoka the Great was incredibly aware of the political situation of the Greek world outside his borders, correctly identifying Antiochos II of the Seleucid Empire, Alexander II of Epirus (all the way in Epirus!), Magas of Cyrene, Antigonos Gonatas of Macedon, and Ptolemy II Philadelphos of Egypt (all of these were transliterated, but the names are very recognisable.) The Greek communities responded to Buddhist missionary activity, and became a vibrant part of the Buddhist communities in Arachosia and India. It is believed that they were possibly responsible for human representations of the Buddha, as previously he was represented in abstract. The Buddha was known as 'Boddo' in Greek, which always sounds a little similar to me. The Greeks had their own spin on Buddhism of course, that incorporated the regular Greek pantheon. This was something of a crazy religion!

To go back to Bactria, it had expanded fairly rapidly. By 180 BC, it had conquered Margiana (which contains the modern city of Merv), Sodgiana (which contains Samarkhand), large chunks of Arachosia in the wake of the collapse of the Mauryan Empire, and was now quite a large entity. So in 180 BC, the Mauryan Empire having mostly collapsed, King Demetrios of course decided to invade India, and succeeded, conquering large swathes of northern India. And now the Hellenic communities of India and Arachosia were again under the rule of a Greek-ruled state.

Things seemed to be going fine for this state until a combination of nasty things; a civil war between the Bactrian royal family and some Indo-Greek rivals was fairly brutal, and this was in 170 BC. This was followed by quite a few defeats by the Parthians, who had begun to esatablish themselves, but a bigger issue was to come; in 140 BC, much of Bactria itself was overrun and destroyed, probably by Saka/Scythians. Twenty years later, Bactria's shattered remains were absorbed by the Yuezhi/Yuechi/Kushans/Tokharoi (an Indo-European people from the Tarim Basin), where they remained for the next century.

The Indo-Greek Kingdom, as it is referred to from about 170 BC onwards, continued fairly happily for the next two centuries, until around the turn of the millenium; the Kushans expanded into India, and absorbed the last independent Greek realms in the east. However, this is not the end of the story; from this point onwards, the Kushans are known as the Kushan Empire; they had already been partly Hellenised themselves in their time in Bactria, and they were using a modified form of the Greek script for their own purposes; Greek cultural artifacts continued to be produced, Greek coins were used, Greek was spoken, and so the Greek communities appear to have continued to thrive in their own way. The Kushan Empire then continued to exist until around 375 AD, when the Indian sections were conquered by the rising Gupta state. In the case of Bactria itself, and Arachosia, that became the territory of the Sassanid Persian state. The last vestiges of Greek material culture and Greek speakers only really vanish around 500 AD, and it's probably that whatever was left of the Greco-Buddhist community in Afghanistan and India was destroyed by the Islamic conquest of those areas (as was the Buddhist community in North-Western India in general). Traces of Greek influence remained for longer afterwards, if you accept that they had an influence on Indian art and culture.

As for Hellenistic Mesopotamia, there were less Greek communities there because the area was already so densely settled. Babylon and many other cities like Uruk remained important in this period, the idea that Seleucia on the Tigris (a city founded on the Tigris river by Seleukos, funnily enough) destroyed the economic and political power of Babylon is incorrect. It was no longer top dog in Mesopotamia, but that's not the same as destroying it. The Seleucid Kings often rewarded people in the region with 'Greek names', which is in interesting insight into a 'deliberate' practice of trying to 'Greekify' people rather than having it happen accidentally. Greek interest in Mesopotamian astronomy was very high, and large chunks of Sumerian/Akkadian mathematics and astrology became adopted by the Greeks. It's around this time that some kind of single, coherent, astrological system appears in the Near East, which is something we still don't fully understand. The Greeks were not responsible for the destruction of native Mesopotamian culture, which was already a mishmash of dozens of cultures by this point anyway, cuneiform continued to be written, temples continued to be founded/rebuilt, foundation cylinders were still placed in buildings by the Seleucid monarchs. I would say more about Hellenic Mesopotamia but my focus really is further east, and I don't want to go beyond the limits of what I actually know. The main historical debate is whether or not the Mesopotamians actively resisted Hellenic culture because they didn't like Greeks, and I don't have an answer for that.

One thing that unifies all of the places settled/controlled by the Greeks is Greek-style buildings that turn up; places like Ai Khanoum and the other Alexandrian/Seleucid founded cities are very much fully formed Greek cities in the middle of non-Greek areas (spectacularly so with Ai Khanoum which has some of the largest Greek architecture of any Greek city in world history yet discovered. The main road in that city was twenty metres across, the palace was 200 metres by 170 metres wide, everything was fairly enormous). But even Babylon ended up with a Greek theatre, nearly every major city ended up with some kind of Greek footprint from Anatolia to India. If you want a really interesting account of experiencing 'Hellenisation', read the Old Testament. Specifically those sections dealing with the Jews under the Greek states, like Maccabees. It is the rare glimpse of a culture expressing its views about the Greeks doing their thing.