The new generation of privacy chains, such as Aztec and Miden, is reshaping how private onchain computation works. Both are built on the core idea of client side execution, where users run transactions locally, generate zero knowledge proofs, and submit only verifiable commitments onchain. This keeps sensitive data offchain while preserving public verification and scalability. Aztec is a privacy-first zk-rollup on Ethereum supporting hybrid smart contracts written in Noir, with both private and public functions. Private logic runs client-side using zk-SNARKs, while public logic executes onchain, enabling private DeFi and DAO use cases through encrypted notes and nullifiers. Miden is a STARK-based zk-rollup with a hybrid state model. Users execute transactions inside a zkVM, generate STARK proofs, and submit minimal state updates, allowing the chain to verify execution without accessing user data.