There are a lot of different iterations of Ascendancy Combo, and over the next few days I am gonna make lists for all of them.
Oh, and also the budget versions, which are not as good but certainly work.
The source of this deck is Channel Fireball and some people who built it.
Here is a version of the list
http://www.channelfireball.com/articles/standard-jeskai-ascendancy-primer/
Let's go through the cards and explain their reason for being here.
Sylvan Caryatid-Not only is it a mana combo piece that generates infinite mana of any color, but it is hexproof, so your combo can stay in tact with those pesky erases in the board of most decks. Admittedly, since it has defender, you will need another creature to attack with, but that is not a problem with cards like Commune with the Gods in the deck.
Kiora's Follower-Tap to untap your land and make floating mana, another mana combo. Also, it can untap your other permanents instead of just your lands. Untap the Springleaf Drum if you want to. Not that untapping is really a problem with this deck.
Rattleclaw Mystic-Yet another combo piece that can attack. Usually a win con like the previous creature that can be targeted with the Retraction Helix to clear the way.
Astral Cornucopia and Tormod's Crypt-The two 0 drop artifacts that trigger your combo. Retraction helix it to your hand, and then commence the combo!!
Taigam's Scheming and Commune with the Gods-The cards that ensure you draw what you need. Without the combo pieces, then you will struggle to win the game.
Jeskai Ascendancy-The key to it all-The only reason this deck is a thing. Fire off the combo by making infinite mana, bouncing nonland permanents to your hand, and just keep on triggering this ability until you pull out with some infinitely large creatures.
Twinflame and Dragon Mantle-Use these cards to make temporary creatures with the first, and then use the second to use your mana and give the enchanted creature infinitely more infinite attack.
Retraction Helix-The other combo piece. Bouncing cards to replay them with your infinite mana. Pretty awesome.
