- micropayment channels -- send money a piece at a time
- cross chain contracts -- bind simultaneous release of funds to a shared secret
- lightning channels -- cross-blockchain stateful commitments
- reputation -- not great but can still work
The order book is another part that can be decentralized. It's a little harder to do this due to the need for high speed communication but I believe its possible. Newer blockchains like Solana have different consensus algorithms that allow for a 'global clock' to be created with minimal bottlenecks. It wouldn't be as fast as everything sitting on a server but its performance would be adequate for traders, IMO.
Bonus section: dark pools could be created with SGX or MPC protocols. There are some popular decentralized exchanges at the moment. But IMO they will need more features that traders are familiar with to be competitive (there's more than just currency pairs and limit orders tbh.)
Also: big shout out to https://www.projectserum.com/