I've read two theories.
Both theories follow the eruption of Thera, but one is, the Mycanean's came in and took over the temple at Knossis, but another theory is the Sea People's drove the Mycenaean's into the mountainous regions, and then maybe the Mycanean's took them over afterwards, or were already destroyed themselves at that point.
I've also read that the Minoans's continued to write under their new rulers the Mycaneans under a new written language since their rulers didn't have their own language; however, after the fall of the Bronze age... writing stopped until Greece. So there is a point where civilization fell apart. I'm trying to figure out where.
It's widely believed that the Mycenaean conquered the Minoans. This is evidenced by the building of Mycenaean style walls which appear in Crete after a certain period and the introduction of Minion aspects into Greek mythology (images such as the Minotaur are believed to be influenced by the fact that Minoans worshipped bulls and the double bladed axe was the primary weapon of the Minoans which was wielded by the Minotaur). There is evidence of fire damage which burned down many Minoan cities around the same time which occurred before the fall of the Mycenaeans.
As for the fall of the Mycenaeans, there really isn't a clear reason as to who destroyed their civilization as the civilization rapidly collapsed and no real records of that time still exist. The Sea Peoples argument comes from Egyptian sources who were attacked by this group around the same time as the fall of the Mycenaeans and the Hittites. Despite this, there is no solid evidence of where these people came from and if they even attacked either the Hittites or the Mycenaeans.
As for writing, the Minoans had their own unique style of writing that even today we cannot decipher. Under the Mycenaeans the Minoans adopted the Mycenaean Linear B script which is also used as evidence of the conquest of Crete by the Mycenaeans.
The era where it all fell apart is known as the Bronze Age Collapse and it saw the collapse of the Mycenaeans, the Hittites and the decreased size of the Egyptians. This occurred ~1100BC and the causes are still under debate by historians.