1. Deck-building game
This new trend of card games was pretty much started by Dominion. The core concept in all these games is that players start with a fixed deck of cards, ten in Ascension. These cards are the shittiest cards in the game, giving very little resources. The point of the game is to buy cards from the table and add them to your deck. The experience of playing these games is not unlike getting the experience of building your deck and playing it, only both at the same time. What could be more awesome?
A careful observer might notice that at its core the mechanic is the same as any other game where players spend resources to produce more resources and do other useful things in the future. This is definitely true. The basic mechanic of deck-building games just makes the process really interesting and smooth. On any given turn, you get five cards out of the cards left in your deck. What's the best use for them? What cards should you get to improve your average hand? Turns are usually over fast. Usually, unless some or another killer combo comes up.
The concept of the average hand is highly important in deck-building games. Since hands are always random, mindlessly buying good cards can actually lead into a very bad deck if those cards don't work together well.
It is also typical to deck-building games that not all the cards in the game are available in each game. Quite far from it actually, as usually the cards available are a rather small subset of all the cards in the game, especially since these games spawn expansions like no tomorrow. This pretty much ensures that no two games are ever exactly alike, and new strategies come up even after hundreds of plays. The downside is that once the amount of cards becomes large, the setup gets a bit annoying.
A lot of these games are mostly multiplayer solitaire, although on occasion there's cards that affect other players.
2. Center row & portal deck
Okay, back to Ascension. Unlike a typical deck-building game, Ascension does not feature a storage that is randomized at the beginning of the game (storage is the pool of available cards). Instead it features a center row with six card slots and a portal deck. Cards are drawn from the portal deck to the center row so that it is always filled with six cards. This mechanical change to the norm has two pros.
First, it hugely decreases setup time (although after the first expansion, shuffling the portal deck does become a bit difficult). Second, whereas in other deck-building games I've played strategies are usually cemented at the beginning of the game (if you change mid-game, you are screwed), in Ascension players have to play more flexibly because there is no knowledge of what cards will be available in the future.
The center row also provides some means for players to affect each others' strategies by buying off or banishing cards they think other players might want. This is much harder to do in other deck-building games because the supply of cards is usually sufficient for all the players to get the ones they really want. Denying players of cards is a viable and often necessary strategy to keep opponents in check.
The flipside of this mechanic is that sometimes the center row does introduce more luck of the draw into the game. There are two basic cards that are always available, but they are not comparable in power to cards from the portal deck. Then again, this is why players need to stay flexible, to make use of the cards available to them on their turn.
3. 2-dimensional economy
Ascension has two resources that the players use: runes and power. The former is used to acquire cards (basically money) and the latter is used to defeat enemies. There are really few cards that provide both, so players need to make choices. Focusing entirely on one is a gamble - if the center row does not favor your strategy, you are majorly screwed. Staying balanced on the other hand makes it difficult to get the best cards or defeat the monsters with the biggest rewards.
Building a deck that does both effectively is the holy grail of Ascension, but quite hard to achieve. To get there, players need to acquire cards that improve the deck's infrastructure but these cards don't usually provide any resources. Decisions, decisions.
Usually cards in deck-building games are only useful on the turn they are played, and then it's off to the discard pile with them (until they come up again once the deck is depleted and the discard pile is shuffled to become the new deck). In Ascension there are constructs that stay in play unless a specific effect discards them. This introduces a new deck type into the game, one that slowly builds these more constant resources (which have weaker effects than heroes) to improve their average turns.
Such a strategy can have huge payoff, but it also poses a big risk if certain effects trigger. It also is blatantly obvious to other players, which makes it easy for them to deny you the cards you need for this strategy.
Ascension differs from most other deck-building games by the portal deck system. None of the game's innovations are new but rather cleverly adapted mechanics from other games. The designers have looked for inspiration outside the deck-building genre and created a highly enjoyable game. Ascension is particularly successful in dealing with the two common problems of deck-building games: setup time and the multiplayer solitaire symptom.