For these, blockchain is only used as a settlement layer while the orders are hosted by centralized third-parties.

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These exchanges use smart contracts for transaction settlement. We can distinguish two types of order book exchanges based on how order books are hosted.

Decentralized order book exchanges

Schär, Fabian, Decentralized Finance: On Blockchain- and Smart Contract-based Financial Markets (March 8, 2020). Available at SSRN: https://ssrn.com/abstract=3571335 or http://dx.doi.org/10.2139/ssrn.3571335 



Decentralized Finance: On Blockchain and Smart Contract-based Financial Markets

Off-chain order book exchanges

In this case, every order is stored within a smart contract, so there is no need for additional infrastructure or third-party hosts. Network fees can be high in this approach because every action requires a blockchain transaction.

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