Ascension

Wow! Cubes
Ascension is the 4th main prestige tier, and is unlocked upon completing Sadistic 1(C10) the first time. When first unlocked, ascension will reward you with Wow! Cubes, which can be used in the Wow! cubes tab. Cubes can be spent on upgrades, or opened for cube tributes, which provide bonuses for just about everything.

Tributes: See Research Guide for guide on this.

Corruptions
Corruptions are also unlocked at C10x1, and provide some sort of disadvantage(depending on which corruption you enable) during that ascension, in exchange they also multiply your ascension score when you ascend, as well as a percent increase of Spirit effect during the ascension. Corruptions will not be worth using until after C11x2. Corruptions can be cleansed anytime during the ascension without any consequence other than losing the score multiplier and spirit bonus inherent in them. It is worth noting that since they provide a benefit on spirit effects during the ascension and can be cleansed anytime then a common strategy to do rune, obtainium, and some challenge runs is to put 'to many' corruptions on to get extra bonuses from spirit runes to boost ants, obtainium, and etc. then cleanse to not lose on everything else from the corruptions, and since the ants, obtainium, and etc. stay the same you will get both benefits if you play your cards right. This tactic is a late game tactic, and most likely will not help you enough to be worth the hassle until after C14.

Blessings
Blessings are sort of greatly more expensive second tier of runes that stay constant through ascensions. Blessings are also unlocked at C10x1. The effects of Blessings increase and decrease with the increase and decrease of rune they correspond with. Blessings do not have specific names in game like runes do, but are generally referred to as the rune they belong to blessing(for instance speed blessing) or as blessing 1/2/3/4/5. Every time you buy a blessing level the price will increase, the price can be represented as price=next level*1e6, with the first level costing 1e6, the second 2e6, etc. Speed blessing provides a multiplier to Global speed, duplication blessing a multiplier to multiplier boosts, prism blessing a multiplier to ant sacrifice rewards, thrift blessing a cost delay multiplier to accelerator boost, and superior intellect(SI) blessing a "Obtainium-->Ant Multiplier Exponent" Current obtainium to the exponent as ant speed multiplier.

In short the two columns mean:

Blessing power: The product of base level of runes and the blessing level

Effect: The bonus type and amount of each blessing

Tesseracts
Tesseracts are the second tier of cubes, gained at 1 per ascension by default, though this can be increased if you have more than 100k Ascension Score. Tesseracts can be opened for tesseract gifts if you have C11x1, similarly to cube tributes; these gifts all provide a percent power boost to their corresponding cube tribute and are named the same, but tribute is replaced with gift. The probability distribution when opening tesseracts is 4/4/2/2/2/2/1/1/1/1. The number of tesseracts you get starts at 1, and increases based on score. Tesseracts can also be used to buy the fifth, and as of V2.1 last tier of buildings, these produce constant ,which divide taxes by $${1+\log(Constant+1)}$$, as well as being able to be used on repeatable upgrades. All constant upgrades have a cost multiplier of 10

Spirits
Spirits are an even more expensive third tier of runes, and are unlocked on C12x1. The effects of spirits increases/decreases with the correspondinging rune, similarly to blessings. The price of each level increases in the same way of blessings, with the equation being cost=next level*1e20. Spirits are also affected by corruptions, as listed in corruptions section. Speed spirit provides a global speed multiplier, duplication spirit a multiplier to cubes on ascension, prism spirit additional levels to crystal caps, thrift spirit a multiplier to obtainium, and SI spirit a percent increase in research 4x9 effect.

Hypercubes
Hypercubes are unlocked with the completion of C13x1 and are the third tier of cubes, and can only be opened for hypercube benedictions, which all provide a percent increase in the power of the corresponding tesseract gift and are named the same, but tribute is replaced with benediction. The number of hypercubes gained is based on score, and cannot be gained with a score under 1e9. The probability distribution of hypercube benedictions is 4/4/2/2/2/2/1/1/1/1.

Platonic cubes
Platonic cubes are unlocked with the completion of C14x1, and can be opened for platonic statues or used in platonic upgrades. Platonic cubes are also score based, and can only be gained with a score over 1.337e12, which means that there is likely going to be a considerable time in between C14x1 and your first platonic cube, it is very unlikely that you will gain platonic cbes until well after C11x30/C12x30/C13x17/C14x30. The probability distribution and effects of opening platonic cubes is 13200/13200/13200/396/1/1/1/1