Skip over verifying everything and only verify a subset of all things you care about. Use alternative root nodes you trust instead of verifying. Stuff like that. They have a spec: https://eth.wiki/concepts/light-client-protocol

It works by surrendering any pretense of eth being a decentralized cryptocurrency and turning every node into a glorified and bloated transport/identity layer.

If you’re not validating transactions - you’re trusting a third party. There are no light clients that avoid this problem. It remains to be seen if they are even possible.

Sorry it took me ages to clarify this. It's actually a pretty cool mechanism! What I mean by "tracking the head of the chain with certainty" means that you don't have any trust assumptions on the head block. If you track the latest head block, that means you can verify Merkle proofs of the chain state (as the state root is a field embedded in a block). This is neat because a light client, using low resource requirements, can tell verify a proof of some state data you present it.

The way it works is that there is a committee of validators in the consensus protocol that is required to sign the head of the chain. We use cryptography known as BLS signatures to perform signature aggregation, meaning you can verify a single signature to ensure that whole committee is correct. The state of the chain can be represented as a Merkle trie, and we can obtain the actual committee as a branch of this tree which can be used during the verification process.

https://medium.com/chainsafe-systems/lodestar-releases-light...

It's really neat and there are working prototypes out there today.