Essentially let’s you verify computation is accurate without doing the computation yourself, and even treating the computation as a black box so you don’t know what is computed. Many applications in privacy, but also for outsourced computation.
One important weakness of zkSnarks is that it requires a trusted setup, for example [1]. A new alternative is called zk-STARK [2], which doesn't require the trusted setup, and is post-quantum secure. However, it significantly increases the size of the proof (around ~50KB). In general, hash-based post-quantum algorithms require bigger size and it would be interesting to watch the progress made in this regard.
If I'm not mistaken, I believe they're found a way for a trustless setup a few months ago. Unfortunately I don't have any more info on hand, but I remember reading that in passing in regards to research performed by Ethereum developers.
Essentially let’s you verify computation is accurate without doing the computation yourself, and even treating the computation as a black box so you don’t know what is computed. Many applications in privacy, but also for outsourced computation.