We survey recent progress in cryptographically verifying computation using zero-knowledge Succinct Non-interactive ARgument of Knowledge (SNARK) schemes. Proposed by Kilian and Micali in the 1990's, such computationally-sound proofs were considered intriguing yet impractical, and invoked mainly for their theoretical implications. Recently, new ideas and schemes lead to both improved theoretical foundations and full working zkSNARK implementations. This talk will discuss these, and in particular:

- Implemented compilers for ensuring the integrity of general computation (e.g., C programs) in the presence of arbitrary platform corruptions.

- A practical application, Zerocash, which solves Bitcoin's privacy problem. Whereas Bitcoin publicly broadcast all transactions and account balances, Zerocash replaces these by privacy-preserving zkSNARK proofs.

Based primarily on joint works with Eli Ben-Sasson, Alessandro Chiesa, Christina Garman, Daniel Genkin, Matthew Green, Ian Miers and Madars Virza.