Here goes...
"Where Buddhas live", not listed because it's inappropriate to call it a realm, but it is inappropriate to say no such realm exists. Buddhas can go wherever they want and take whatever form or formless, subtle or gross state they want without restrictions or karmic effects. And not "want," in the sense of either intention or desire.
- Formless realms: one for each of the four formless jhanas. Just mind, no body.
- Form realms: Physical places (not in our universe, though); you get a subtle body, because of subtle desire (for form) rather than sensual desire (for particular sense-pleasures).
- Pure Abodes: Place for non-returners. From lowest to highest: Not-falling, untroubled, beautiful, clear-seeing. All are not-falling, but you can be not-falling, but not necessarily untroubled, beautiful, or clear-seeing. You can be not-falling and untroubled, but not necessarily beautiful and clear-seeing, etc..
- Other four immaterial realms: One realm for each jhana of form, sub-divided by the immaterial jhana they connect with most. (Only 3 sub-divisions, not the expected 4 because it's not possible to have the jhana of nothingness combined with anything but the fourth jhana, because you can't perceive nothing and form at the same time. And even if you could, that would be neither perception nor non-perception. And only if the fourth jhana is sufficiently strong enough.)
- Desire realms: Where we are. You get a gross body (a sensual body?), because of sensual desire.
- Upper desire realms are associated with the creation of objects of desire (where objects of creation are truly made; in the lower realms, it is merely a manifestation). Mara lives here (the desire realm is regarded as his domain), but the beings in this realm are not all necessarily malevolent.
- Lower desire realms are primarily concerned with using and consuming these objects, the physical act of creation and for taking credit for their creation.
- Realms of Sumeru: The five\six realms of Samsara we're probably familiar with. Places for beings concerned primarily with sensual desire. Sub-divided according to the types of sensual desire which tend to correlate.
- Upper realms of Sumeru: Devas concerned, not with creation in general, but specifically with the governance of the human realm (the sky, moon, sun, time, planets, etc.). As extraordinary as that sounds, their power is very limited. Devas are generally more blissful, asuras are generally more negative, and the two are opposed, while the Four Great Kings are equanimous.
- Human\Earth realms: No idea why there's four of them. Separated by cakravadas... something like the universe's event horizon?
- Woeful realms: Animal realm (ignorance), Preta realms (great pity for one's self and hunger), hell realms (a great hatred for self & others and outrageous greed).
- Realms of Sumeru: The five\six realms of Samsara we're probably familiar with. Places for beings concerned primarily with sensual desire. Sub-divided according to the types of sensual desire which tend to correlate.
