This talk will explore the possibilities for privacy-preserving smart contracts in terms of both cryptography and functionality. It will give an overview of known approaches, including a detailed discussion of zk-proof based schemes such as Zexe (my own work) and an overview of other approaches including refereed computation as seen in systems like Truebit and Arbitrum, multi-party computation, secret sharing, and fully homomorphic encryption. More fundamentally, it will explore what a private smart contract really is. Do we need to hide which contract is running? Do we really want perfect privacy in most cases?