There are two primary types: Optimistic Rollups and zk-Rollups.
According to Newcomb, Optimistic Rollups, as used by Optimism and Arbitrum, ultimately depend on a sophisticated game theory, which effectively allows everyone to use the blockchain. “And then, after the fact, they check to make sure that there is no fraud.”
With this system, “you could be maybe 99.999% sure there’s no fraud, but you can’t be 100%. It’s the very best game theory we have, and it does scale Ethereum by a factor of seven, maybe up to 10.” Though he concedes that it passes as a scaling solution, Newcomb expresses concerns about settlement times at increased levels of scaling, describing the process as increasingly “hairier” and saying that he “couldn’t understand how it scales beyond the original 10x.”
Zk-Rollups, on the other hand, “check for fraud using mathematics — something called a ZK proof that isn’t 99.999% accurate. It does not use game theory. It is literally mathematically perfect.” There are competing zk-Rollup layer 2s from ConsenSys, StarkNet and Polygon.