We survey the state-of-the-art non-interactive zero-knowledge argument schemes and their applications in confidential transactions and private smart contracts on blockchain. The main goal of this paper is to serve as a reference for blockchain application developers in finding the most suitable scheme for a particular use case. We give an overview and compare the state-of-the-art protocols for confidential transactions and private smart contracts regarding the protection of the transaction graph and amounts, data and functionality. However, our main focus is on state-of-the-art zero-knowledge argument schemes. We briefly describe their backgrounds, proof lengths and computational complexities and discuss their cryptographic security models. Our focus is on seminal, otherwise notable and, especially, implemented methods that are ready to be applied in practice. We also survey the existing implementations of transforming computations into circuit representations required by those methods. We note that the existing schemes have different strengths and drawbacks regarding usability, setup, proof length and proving and verification costs.