Explore the critical issue of privacy in blockchain technology through this 19-minute conference talk from USENIX Enigma 2022. Delve into the innovative computation model introduced by cryptocurrencies and blockchains, and understand the significant privacy concerns associated with permissionless public blockchains. Learn about the risks of financial activity tracking, pseudonym address linking, and sensitive data disclosure in smart contracts. Examine current solutions, technology trends, and existing gaps in blockchain privacy. Gain insights into the evolution of blockchain technology, including the birth of Ethereum and smart contracts. Analyze various approaches to privacy, from off-chain to on-chain private computing, and consider the challenges of concurrency, multi-user inputs, and efficiency. Conclude by contemplating the future path towards viable privacy solutions for private computations over blockchains.