A settlement on the island of Thera was destroyed during the Bronze Age. From ash from that explosion which landed on Greenland, an estimated date of 1628 B.C. was calculated about 20 years ago. The Minoans and Mycenaeans may have been literate, but we have no historical texts from either society. Most of the surviving Linear A and Linear B records are palace records (inventories and the like).
There is no Thera signature in the Greenland ice cores from the 17th century. There's an ash layer over Akrotiri, but no human remains have been found, suggesting abandonment prior to the eruption. There's no link between the end of Minoan palatial civilization and the supposed (but unattested) super-eruption; what is found instead is not tsunamis or earthquakes, but fire, showing destruction by human hands. Even before the latest backdating of the supposed super-eruption (from 1500 BC to 1628 BC or whatever), the Palatial civilization continued with no apparent ripple for 80 years, and now the much-delayed reaction to Thera is claimed to have taken place as much as 200 years later.
Where the Minoans had been, the Mycenaeans took over, which is difficult to explain since the supposed tsunami supposedly caused by the supposed super-eruption and caldera collapse would have been directed toward mainland Greece, rather than Crete. The archive of Mycenaean Pylos -- which is centuries after the supposed super-eruption -- actually ends with a scrawl of Linear B recording where the troops were being sent and a record of a man and woman being sacrificed to propitiate their gods.
"Even when, during the respective Thera Conferences, individual scientists had pointed out that the magnitude and significance of the Thera eruption must be estimated as less than previously thought, the conferences acted to strengthen the original hypothesis. The individual experts believed that the arguments advanced by their colleagues were sound, and that the facts of a natural catastrophe were not in doubt... All three factors reflect a fantasy world rather than cool detachment, which is why it so difficult to refute the theory with rational arguments." -- Eberhard Zangger, "The Future of the Past", pp 49-50.