ZKPs have recently been implemented in Zcash successfully, as seen in Chapter 8, Alternative Coins. More specifically, SNARK (short for Succinct Non-Interactive Argument of Knowledge) have been implemented in order to ensure privacy on the blockchain.
The same idea can be implemented in Ethereum and other blockchains also. Integrating Zcash on Ethereum is already a very active research project being run by the Ethereum R&D team and the Zcash Company.
The original research paper is available at https://eprint.iacr.org/2013/879.pdf.Another excellent paper is here http://chriseth.github.io/notes/articles/zksnarks/zksnarks.pdf.
There is a recent addition to the family of ZKPs called Zero-Knowledge Succinct Transparent Argument ...
