Crete changes hands (not for the last time)
Pithoi at Knossos
The events of 1450 mark a point at which it’s clear that Minoan power was in decline. As in 1700, it looks as if an earthquake knocked down the palaces, but they were also burned, leading many historians to believe that invaders might have lent a hand in the process. As George Papadopoulos pointed out to us, however, every palace complex included lots of closed storerooms full of huge clay jars—called píthoi in Greek, though of course we don’t know if that’s what the Minoans called them—some of the jars filled with grain and others with olive oil. The only light in those dim chambers came from small oil lamps. A drastic seismic shock would have smashed the jars, and only one burning lamp would have to fall into the resulting puddle of oil to start a serious blaze.
So we don’t need hordes of howling barbarians to explain the burning of the palaces. But there are further reasons for wondering if the barbarians might have been on the scene. The only palace rebuilt after the destruction of 1450 was Knossós, which continued to be a center of authority, on some level at least, until 1325. During those 125 years, however, all records kept there were inscribed in Linear B rather than Linear A—that is, in Mycenaean Greek rather than the Minoan tongue.

There's good reason to believe that the Mycenaeans created Linear B on the model of Linear A, even though their language was was nothing at all like the Minoans'. Many of the characters look similar, and I found a statement on the Web (which I haven't verified) that there's about a 70% overlap between the character sets. If true, that’s enough to show that the similarities are not coincidental. I couldn’t find tables that make it easy to match the characters, but if you'd like to try, or just get a general idea of the similarity, click the button below.
Approximate extent of Mycenaean-ruled territory
No one has found written or archaeological evidence of an invasion from Greece in that period on a large enough scale to overwhelm the whole island of Crete in one go. Some have theorized that there was a popular uprising by the Minoan masses, the burning of palaces implying a kind of targeted hostility to their rulers. I’m more inclined to accept George’s explanation for the burning; if he’s right, palaces were about the only places where oil was stored in large enough quantities to cause devastating fires when ignited by a falling lamp. That could be the reason why palaces burned and other places didn’t.

The dark line on the map shows the approximate extent of the territory controlled by the Mycenaeans at the height of their power. (The city names are mostly from the later classical period.) However it came about, Mycenaean dominance of Crete from at least 1450 onward is clear. If there was a popular uprising, some rebellious local group could have invited a Mycenaean king or warlord to help them in their struggle, and learned too late that the cure was at least as bad as the disease. Or some Minoan magnate, feeling threatened by unrest among the lower classes, could have learned the same lesson after surrounding himself with a corps of Mycenaean mercenaries.

Here’s another possibility: for several centuries, the Mycenaeans had been avidly learning from the Minoans and emulating whatever qualities of Cretan civilization were compatible with their own warrior culture. Over time they became powerful not only on the mainland, but on the Aegean as well. Perhaps there were Mycenaean settlements in Crete that began as trading colonies well before the time when the palaces went down in rubble and up in flames. During the difficult years when Minoan strength and self-confidence were declining, the newcomers’ strength, confidence and—most significantly—numbers might have been growing. And perhaps, after the seismic calamity of 1450 proved to be the last straw, the demoralized Minoans were inclined to say to them (in whichever language was appropriate) “OK, that’s it. We’ve had enough. Why don’t you take over for a change—you can hardly make things worse.”

However the change took place, the succession of writing systems tells the story. A quick Google search suggests that no examples of Linear A have been found that were written later than 1400, and the earliest surviving examples of Linear B date from 1375, only 25 years later (although some writers, on what evidence I don’t know, give 1500 or even 1600 BCE as the approximate date when Linear B began to be used).
Warriors marching around a vase found at Mycenae
Some scholars have suggested that there never was a Mycenaean conquest, but only a local adoption of Mycenaean customs and artifacts. However, the Mycenaeans certainly did get to Crete in substantial numbers, whether suddenly or gradually. Nothing else would explain the change of language. For the Minoans to abandon their own tongue and adopt one that hardly anybody in Crete knew how to speak seems very unlikely.

The earliest Linear B inscriptions are dated no earlier than 1375 BCE, only 50 years before the final destruction of the palace at Knossós, where some of these inscriptions were found. However, a good many have turned up elsewhere in Crete, and it’s clear that business (the subject of most Linear B texts, in the form of inventories and the like) was being carried on in Mycenaean Greek. Whether they achieved this by warlike or peaceful means, the Mycenaeans were now running the island.

However, the Minoans didn’t disappear all at once. Greek texts (including the Iliad) refer to a people called Eteocretans (‘true Cretans’) who shared the island with the Achaians (another name for Mycenaeans) and the Dorians (soon to appear in this narrative). In the same passage Homer describes Crete as a place where several languages coexisted. A few Cretan inscriptions have been found, written in an early form of the Greek alphabet—which didn’t yet exist in Homer’s time—that are clearly not in Greek. These are thought to represent the Eteocretan language. which most scholars believe twas Minoan, or something descended from it. Unfortunately, however, the inscriptions, from between the 7th and 3rd centuries BCE, are too few, too short, and too fragmentary to yield any reliable information about the nature of the language, much less the meaning of the words. Still, if the scholars’ guess is correct, the inscriptions do testify to the survival of Minoan ethnicity and culture in Crete for upwards of a thousand years after Minoan power came to an end.