A step (but not necessarily a giant step) backward
If the Mycenaeans did in fact conquer Troy it happened early in the 1100s BCE, that is, not long after 1200. (Remember that before the Common Era we’re counting backwards, so the lower numbers are the later ones.)

The conquest of Troy may have been the Mycenaeans’ last hurrah. By the end of that century (i.e. by 1100 BCE) all their cities had been burned, and the Mycenaean “empire” (which in fact had never been more than a cluster of separate kingdoms often at war among themselves) had perished, its culture as dead as its power. The infant technology of writing was lost, and for more than 400 years—until the Phoenician alphabet was borrowed and adapted to the writing of Greek—nothing that was happening in the Greek-speaking world was recorded in writing. Historians, frustrated by the complete lack of documentation, have named this period the Greek dark age. (Dark here means ‘obscure,’ not ‘ignorant’ or ‘evil.’)

When written records once again shed light on Greek history, starting in about 800 BCE (give or take 50 years), most of the lands formerly occupied by the Mycenaeans, Crete included, have been settled by a Greek-speaking people called the Dorians.

The standard interpretation, until fairly recent decades, was that the Dorians (a warlike but—compared to the Mycenaeans at the time of their collapse—culturally less advanced people) had entered Mycenaean territory from their homeland in the northwest (the modern Greek region of Epirus and perhaps some adjoining parts of Albania and Macedonia) as invaders, taking and burning the proud Myceanean cities, apparently undeterred by their massive Cyclopean walls.
Herakles with Athena
Ancient Greek tradition gives support of a kind to this thesis: a legend relates that the mythic hero Herakles, who belonged the royal Perseid house, had been expelled from the Peloponnesus by the children of the rival house of Pelops—said children being founders of the dynasties that ruled the Mycenaean kingdoms. In the legend, Herakles’ sons and grandsons struggled to recover his lost inheritance, and his great-grandsons finally succeeded. The story describes the struggle as a series of single combats between leaders rather than large battles between armies. The victorious great-grandsons are the legendary founders of the Dorian states, such as Lakonia and Messinia, that replaced the fallen Mycenaean kingdoms. This picture, on a kylix (drinking cup) from the classical period, shows Herakles in his customary lion-skin attire being poured a drink by the goddess Athena. (That would be her helmet on the table. She never went anywhere without it.)

But, regardless of legend, archaeology hasn’t been able to support this interpretation. The Dorian movement to the southeast looks much more like a migration than an invasion. It’s now more commonly thought that they occupied what had been Mycenaean territory only after the collapse of the society that had ruled it. The fires that burned the cities had been set by someone else. But who?

According to one theory, it was the Mycenaeans themselves, wiping out each others’ kingdoms in suicidally destructive wars. This is certainly possible; there’s plenty of evidence that they often fought one another—but not enough to prove that they finished themselves off without outside help.
'Sea People' warriors captured in Egypt
Another theory invokes the Sea Peoples, a somewhat mysterious confederation of mixed ethnicities who wrought a great deal of havoc in the eastern Mediterranean region during the 1100s BCE. They’re said to have polished off the Hittite and Mitanni empires in Asia Minor and several small kingdoms on the coast of modern Syria, and they challenged the Pharaohs for control of Egypt. In this last enterprise they failed; the ones who invaded were defeated and taken captive by Ramesses III, and were, many believe, ultimately given land to settle on in what’s now the Gaza strip, where they became the Philistines of Biblical fame. (Interestingly enough, their pottery has strong resemblances to Mycenaean pottery, raising the possibility that the roaming Sea Peoples may have included some of the losers of those internecine conflicts in their homeland.) The picture, from Ramesses’ funerary temple, shows some Sea Persons who were rounded up as prisoners of war after the pharaoh’s victory.

One point sometimes made in arguing that a Dorian Blitzkrieg wiped out the Mycenaeans is that the Dorians used iron weapons while the Mycenaeans relied on bronze. This is not because iron weapons were superior in themselves; iron making was still in a relatively early stage of technical development. But iron was easier to obtain; there were plenty of deposits around, while bronze making required rarer and more expensive supplies of copper and tin. Iron spearheads could be cast in quantity, so larger armies could be equipped. Massed infantry became more than a match for individual heroes like those Homer describes, fighting from chariots. But, alas for this argument, it appears that the Dorians’ general adoption of iron weapons happened some time later than the destruction of the Mycenaean cities, at a time when ironworking was becoming common throughout the Mediterranean world.

Recognizing that I’m in no position to settle a dispute among scholars who know much more about the subject than I do, I’m going to leave it at that.

Because the Dorians spoke a distinct Greek dialect, we can identify the areas they occupied by looking for places where that dialect was spoken in later times for which documents exist. When writing reappeared almost 500 years after the disappearance of Linear B, it employed the newly invented Greek alphabet. The alphabet, as well as the spoken dialects of Greek, evolved gradually over time, with considerable regional variations. The spread of literacy produced many records that survived to show what was being spoken in every part of Greece, and how it was being written down.
Greek dialects in the classical period
Here is a map showing the distribution of Greek dialects during the classical age that produced most of the literature and architecture we think of when we hear phrases such as “the glory that was Greece.” (The conventional dates for that age are from about 500 to 300 BCE, so it's at least 500 years after the Dorians became the dominant population in Crete.) The dialect areas where “Doric proper” is spoken are colored light brown on the map. They include parts of the Peloponnesus plus all of Crete and several smaller islands, including Rhodes and the mainland peninsula north of it, where Greek settlers established the city of Halicarnassus, later home to one of the seven wonders of the ancient world: the Mausoleum (i.e. the tomb of king Mausolus [Μαύσωλος]). There's also a light brown patch in the upper right corner of the map, where Dorians settled on both sides of the Bosphorus and founded the city of Byzantium.

To the north of “Doric proper” are dialect areas labeled “Northwest Doric” and “Achaean Doric,” probably reflecting linguistic changes that happened after the southward migration, among the people who didn’t take part in it.

As far as Crete is concerned, the dialect evidence is very clear that it’s one of the areas settled by Dorians in sufficient numbers to establish their variety of Greek as the standard spoken language.

There’s no evidence that the Dorians took Crete by violent means; it looks much more likely that they settled there peacefully enough, and that by 1000 BCE they had become the dominant population. That’s about all we know regarding the Cretan Dark Age.

In time, according to the Rough Guide, Crete followed mainland Greek civilization as it advanced out of that obscure period (which ended, according to convention, about 750 BCE and was followed by the archaic period, which lasted until the classical period began in about 500 BCE. Crete (again according to the Rough Guide) lagged a few steps behind mainland Greece in its cultural development during these centuries, but it did adopt the art styles and technologies, like ironworking and toolmaking, that spread through the Greek world under cover of the age's supposed darkness. Politically, the island was full of independent and contentious city-states frequently at war with one another. Górtys was among the most powerful; perhaps that’s why Homer put it on his list of eminent Cretan cities without its having (as far as we can know for sure) a Minoan pedigree.
Laws inscribed on Górtys wall
In about 450 BCE, the rulers of Górtys had the laws of their city carved on a wall where the now-literate citizens could refer to them, and—fortunately for us—the Romans, who ruled the city much later, used the stones of the fallen wall for constructions of their own and thus preserved the inscription. It’s the earliest and most complete of the Greek law texts surviving from that archaic period. The picture shows a section of that wall. (If you enlarge the picture and look closely, you can see that the lines read from left to right and right to left in alternation, like an ox plowing a field—in fact, the name for this style of writing was boustrophedon, or ‘ox-lined.') Górtys’s laws reflect a society rigidly structured in classes: rulers, serfs, and slaves. The life prescribed for the rulers has been described as “a harsh, militaristic regime, similar to that of Sparta”—which was also a city of Dorians.

All Greeks still respected the island as the homeland of some of their most ancient historical and religious traditions: two Cretan caves associated with the birth and infancy of Zeus attracted many pilgrims. But the mainlanders also considered Crete rather backward—according to the Rough Guide, “a den of thieves and … a valuable source of mercenaries unrivaled in guerilla tactics.” The guidebook doesn’t mention the Cretan specialty of archery, but Crete was famous for its skilled archers, who were hired to serve in many Mediterranean armies—for instance, those of Alexander the Great in the 4th century BCE. It seems that archery, an ancient skill, had been diligently preserved by the Cretans while other peoples were letting it lapse in their concentration on newer military methods. Probably most of those Cretan mercenaries, regardless of their mastery of guerrilla tactics, were hired as archers.
Spartan plate with mounted warrior, early classical period
However, some Greek philosophers admired Crete for its strict Doric political structure. Athenian politics made quite a few of that city’s philosophers highly sensitive to the shortcomings of democracy, and more than one expressed the wish that Athens could be more Doric—like, say, Sparta.

But the Spartan plate pictured here, dating from early in the classical period, suggests that Sparta’s culture may not have been utterly devoid of lyrical elements. It shows a mounted warrior attended by a winged goddess (perhaps Níke, or ‘Victory’) and several birds, presumably of good omen. The subject is Spartan enough, but the style seems less so—at least according to the presumptions of our own age.

Historical texts don’t offer us a lot of information about Crete during succeeding ages (after the dark age, which ended around 800 BCE, came the archaic, the classic and the Hellenistic periods). The slow growth of civilization went on, but the island doesn’t seem to have done much during these centuries to impress itself on the world’s attention.