There was a mention in Frazer's The Golden Bough in which Greeks pointed out that upon death, people are presented with the option of drinking from the Fountain of Mnemosyne (to forget) or a Goblet of Remembering (to learn and move on). I cannot locate an online reference for that, but I highly recommend downloading the Librevox audiobook of it for free and giving it a listen. It covers many topics and is very good, especially areas which focus on death. It is a loooong book, but worth it.

Specifically, the river Lethe is one of the boundaries a person crosses after dying.

https://en.wikipedia.org/wiki/Lethe

It focuses on memory loss, while some of the other rivers, like Acheron, is for woe, and Styx is sort of the general purpose river. In any case, it is interesting that Mnemosyne fountains (the one mentioned above) are considered to be fed by the river Lethe:

https://en.wikipedia.org/wiki/Mnemosyne

And, to no surprise, people become Shades when they drink from Lethe

https://en.wikipedia.org/wiki/Shade_(mythology)

And, specific to this, Virgil writes in the Aenid that only after becoming a Shade, can one reincarnate on Earth. It's part of the deal.

Long story short, this example of Greek mythology being a small vignette into the idea of katabasis

https://en.wikipedia.org/wiki/Katabasis

While keeping in mind that mythological differences between cultures can generally be attributed to an underlying truth which is filtered and understood by the people of their time, the Greek concepts are remarkably similar to that of other cultures.

You will find many surprising parallels to the work of those old thinkers to the people of today in online discussions/subreddits like this one who have never studied those old Greeks (and others). People tend to arrive at similar conclusions.