What do you think of the improbably long lifespans referenced in the Bible?

The Bible claims many of its Old Testament characters lived very long lives—hundreds of years long. I’m curious what your thoughts are on this? If you literally believe in this how can you justify the extreme difference between Old Testament life spans and modern lifespans. If you’re not so inclined to believe Methuselah reached his 969th birthday, why do you think it was claimed he did in the Bible?

Feel free to refer to other religious or mythological references to improbably old people.