We don't know anything much. To give an idea of how speculative the available theories are, here's a list of potential explanations that have been suggested by various parties, specifically for the collapse of the Mycenaean palace culture, collected by Guy Middleton (Collapse and transformation. The Late Bronze Age to early Iron Age in the Aegean, 2020, p. 13):

1. Civil war (war between parties within a polity).

2. Climate change and drought (aridification, 'megadrought’).
3. Changes in warfare (from chariot to foot-soldiers, undermining palace power).
4. Decentralisation (power/trade moves from palace centres to others).
5. Earthquakes (major earthquakes/earthquake storms over several years).
6. Economic change (e.g. changing trade routes/access to goods).
7. Environmental damage (deforestation/reducing carrying capacity/basic subsistence/palace income).
8. Faction (divisions and competition at elite and ruling elite levels).
9. Failure of integration (either general population/local elites/territories).
10. Food shortages (often attributed to drought).
11. Hegemonic failure (expanding/imperial states fall apart/failed expansion).
12. Ideological failure (loss of faith in the dominant ideology that underpins society).
13. Invasion/migration (Dorians, non-palatial Mycenaeans, Northerners, Sea Peoples).
14. Interstate/interregional conflict (wars between Mycenaean states/non-states).
15. Overcentralisation (rigid, ‘totalitarian’ systems unable to cope with changing circumstances).
16. Overcomplexity (leading to forced simplification).
17. Overpopulation (exceeding environmental carrying capacity).
18. Overshoot (environmental issues + overpopulation = reduced carrying capacity).
19. Overreach (military/political overextension = failure and instability).
20. Plague (affecting the population, economy, faith in gods/ideology/rulers, opportunities for enemies/revolt).
21. Revolt (elite/peasant/provinces/slave/vassal states).
22. Royal succession (division within extended royal families/harem conspiracies).
23. Shortage of bronze.
24. System collapse (fragmentation of palatial system).
25. Trade changes/disruption (whether locally or in eastern Mediterranean; affecting wealth economy).
26. World-system collapse (eastern Mediterranean ‘system’; affecting wealth economy).

Most of these only affect the Mycenaean palace culture, and ignore the collapses seen elsewhere: you can't blame the Hittite 'collapse' on imaginary Balkan invasions of Greece, or on domestic Greek political trends. Some of these suggestions are even more localised (earthquakes).

At the other end of the scale, more global explanations like plague (number 20), shortage of bronze (number 23), and 'world-system collapse' (number 26) are speculative (there's no evidence for them) and also too broad: trade didn't suddenly disappear from the eastern Mediterranean, including trade with the Greek world; and other large eastern Mediterranean cultures were not affected by such things. Some hypotheses in the middle, like megadrought (supported e.g. by Eric Cline), seem like better candidates, but different parts of the Mycenaean and Hittite regions show different kinds of evidence: Hittite documents contain references to famine, but Mycenaean documents suggest perfectly normal levels of food supply (Middleton, p. 14).

It's telling that when people do try to cite direct indications of collapse, they point to evidence from Egypt (the 'Sea Peoples') ... a culture that did not collapse.

Here's how Middleton concludes.

... it remains difficult to describe more than that there was a relatively widespread set of destructions at major centres and significant culture change ... With such a bare picture of events and history, it is then difficult to offer convincing explanations for why such changes occurred.

In the rest of his conclusion he makes it clear that he thinks the Mycenaean collapse is a specifically Mycenaean phenomenon, not part of a more widespread event. That's a little hard to swallow, but the possibility has to be admitted. It could be for example that the Hittite 'collapse' shouldn't really be seen as a collapse as such, but as a fragmentation of their empire -- more similar to the temporary contraction that we see in Assyria, rather than to the destruction that we see in Greece. Hattusa was abandoned before it was destroyed. The only actual destruction that we see outside the Greek world at that time is in Syria, in and around Ugarit. Still, the opposing view, that these events are connected to events in Greece, is still held by some scholars such as Eric Cline.

The short answer is that the inferences and hypotheses continue to flow, but no substantive new evidence has appeared or is likely to appear. One thing that is certain is that the collapse is hugely overblown: some people have got it into their heads that it was a vast continent-spanning event, but in fact it only affected a relatively small region. Exactly how small -- should we be talking about Greece + Anatolia + Syria, or are they separate stories? -- is open to debate.

Edit: an important 'not' was omitted