Single Unified Auction for Value Expression
The best case for Suave from Vitalik -
https://youtu.be/fAgrIdyWIqc?si=DMWxeTuZ0ObYQ69Y
A modification of EVM with precompiles for MEV use cases
Its ambition is to offer every primitive of the MEV supply chain as a precompile in smart contracts
MEVM smart contracts
Can get Ethereum mainnet state, simulate bundles, and make blocks available to proposers using precompiles like getState(), simulateBundle(), and exportBlock().
SUAVE is aiming to provide low latency, privacy, credible computation, and composability so that application developers from the existing MEV supply chain can rebuild their applications as smart contracts on SUAVE. These appl include -

Execution Nodes
The MEVM offers privacy and efficiency by moving compute on sensitive data into execution nodes that run off-chain. Execution nodes provides credible and private off-chain compute that can be used in smart contracts on SUAVE through special precompiles.
SUAVE Chain: a modified EVM chain with MEV-specific precompiles designed for usage alongside credible off-chain execution facilitated by execution nodes. The chain is used for the deployment of smart contracts and for coordination between parties. In the future, the chain will also escrow funds used to pay for preferences, for oracle updates, and data availability.