Monero is a cryptocurrency which claims to be “private, and decentralized”. One of Monero’s main tools towards this privacy is the ring signature. Ring signatures allow you to sign on behalf of a group, without revealing which member of the group you are. They can be constructed as an elegant extension of Schnorr signatures, and aren’t all that hard to understand either.

The ECDSA signature scheme is quite ubiquitous, used everywhere from TLS to various cryptocurrencies like Bitcoin. Funnily enough, it turns out that it suffers from a few malleability issues, although I doubt these pose a serious issue in practice.