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Exchanges can be centralized or decentralized.
Centralized exchanges are businesses that let you buy crypto using traditional currencies. They have custody over any ETH you buy until you send it to a wallet you control.
Decentralized exchanges are open marketplaces for ETH and other tokens. They connect buyers and sellers directly. Instead of using a trusted third party to safeguard funds in the transaction, they use smart contracts to ensure that the seller's ETH will only be transferred when payment is guaranteed.
Read more about Exchanges at Ethereum.org