MEV refers to the total amount of Ether miners can extract from manipulation of transactions. This manipulation can come in a few forms, but most tend to be through re-ordering of transactions within blocks produced and generalized frontrunning.
The three most common examples of MEV are: DEX arbitrage, liquidations, and sandwich trading
MEV-Geth, a proof-of-concept for permsisionless MEV extraction, was recently designed and implemented by Flashbots with the goal of relieving network congestion caused by frontrunning and backrunning bots.
MEV-Boost separates the role of PoS validators: block building and block proposal. Searchers will send bundles to block builders, or they may be block builders themselves.
OpenMEV is a platform for facilitating aggregation and direct communication between block producers and validators. The goal is to allow users to partake in MEV revenue opportunities.

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The Tie Research

MEV: An Intro to Value Extraction