This post written by Vitalik himself, discusses the implementation of Verkle Trees (as opposed to Merkle Trees) on the Ethereum blockchain.
https://vitalik.ca/general/2021/06/18/verkle.htmlTL;DR Verkle trees are a powerful upgrade to Merkle proofs that allow for much smaller proof sizes. Instead of needing to provide all "sister nodes" at each level, the prover need only provide a single proof that proves all parent-child relationships between all commitments along the paths from each leaf node to the root. This allows proof sizes to decrease by a factor of ~6-8 compared to ideal Merkle trees, and by a factor of over 20-30 compared to the hexary Patricia trees that Ethereum uses today.
