There's lots to say on the topic, but check out the AMA with Eric Cline, who wrote a book summarizing current opinions on the topic. Also, I wrote about this yesterday.
It's always helpful to clarify what we mean by "collapse," which ancient historians (and pop history books and podcasts) do not always do. What exactly is it that collapses? What makes "collapse" different from "transformation" or "change"? There's a tendency to telescope the end of the LBA. It should always be kept in mind that the transition from the Bronze Age to Iron Age took well over a century; this was not a sudden apocalypse.
"Collapse" is often associated with notions of cultural regression - de-urbanization, an abandonment of writing, decline in artistic production/quality, disappearance of languages and religious cults, etc. - that we don't see in many parts of the eastern Mediterranean. What collapsed were political institutions, the networks of diplomatic, trade, and imperial interconnections that held together the territorial states of the Bronze Age.
If we choose to consider the end of the Old Kingdom in Egypt a collapse, for example - and I think we should - we can associate it with the slow decline of royal power and the concomitant rise of the nomarchs (regional governors), whose offices were inherited by their offspring. This political shift was compounded by a drought around 2200 BCE, which greatly reduced the agricultural surplus on which the Old Kingdom economy relied. Over the course of the 6th Dynasty, Egypt slowly shifted from a unified state to a highly fragmented political landscape. Rather than a king, Egypt was ruled by competing nomarchs, each ruling his own miniature kingdom and adopting many of the trappings of royal ideology. Put another way, if one thinks of Egyptian society as a pyramid with the king at the top and the nomarchs beneath him, you've essentially removed the topmost layer of the pyramid while leaving the rest of the administrative structure relatively intact.
A similar process occurred in the New Kingdom. There was a slow decline in royal power in the latter part of the New Kingdom, whereas the wealth and power of the Amun priesthood in Thebes grew steadily. We know from administrative texts like the Great Harris Papyrus that temples gained about 15% of the arable land in Egypt in the 19th Dynasty; since temples like Karnak already had massive estates, the total amount of land held by temples was far higher than this. Although Egypt was divided in the 21st Dynasty between a northern kingdom (based at Tanis) and a southern kingdom (based at Thebes), however, we shouldn't necessarily think of these as competing kingdoms. In fact, there was a considerable amount of trade and intermarriage between them. The Tale of Wenamun, for example, tells the story of a priest sent on a mission by the High Priest of Amun. He encounters the king and queen of northern Egypt along the way.
On the day of my arrival at Tanis, the place where (King) Smendes and (Queen) Tentamun are, I gave them the dispatches of Amen-Re, King of the Gods. They had them read out before them and they said: "I will do! I will do as Amun-Re, King of the Gods, our lord, has said."
I stayed until the fourth month of summer in Tanis. Then Smendes and Tentamun sent me off with the ship's captain Mengebet, and I went down upon the great sea of Syria in the first month of summer, day 1.