Under the hood, an optimistic rollup runs its own execution environment: a sequencer orders and executes incoming transactions offchain, then a batcher compresses that activity into a single transaction data blob and a new state root, which gets posted to the underlying Layer 2 settlement chain. Rather than proving correctness upfront with cryptography, the protocol simply publishes the result and trusts it by default, which is what makes the model "optimistic" and comparatively cheap to run.
That trust is backed by a challenge window, historically around seven days, during which independent watchers can re-execute the batch and submit a fraud proof if the posted state root doesn't match. A successful challenge rolls the chain back to the correct state and penalizes the sequencer that submitted the bad batch; if no one disputes it in time, the batch finalizes as valid. This design shifts the cost from constant proof generation to occasional, adversarial verification.
Arbitrum and Optimism remain the largest optimistic rollups by value secured, and both have matured their fraud-proof systems considerably: Arbitrum's BoLD upgrade and Optimism's Cannon fault-proof system now let any party submit a permissionless challenge rather than relying on a whitelisted set of validators, a milestone analysts call "Stage 1" decentralization. Base, built on the OP Stack, inherits the same mechanism.
The main tradeoff is withdrawal speed: funds leaving for Ethereum must wait out the challenge period unless a user pays a liquidity provider for an instant, fee-discounted exit. This is the opposite tradeoff made by zero-knowledge rollups, which prove validity instantly but require heavier cryptographic infrastructure.