Privacy is important to financial industry, so as to blockchain based cryptocurrencies. Bitcoin can provide only weak identity privacy. To overcome privacy challenges of Bitcoin, some privacy focused cryptocurrencies are proposed, such as Dash, Monero, Zcash, Grin and Verge. Private address, confidential transaction, and network anonymization service are adopted to improve privacy in these privacy focused cryptocurrencies. We propose four privacy metrics for blockchain based cryptocurrencies as identity anonymity, transaction confidentiality, transaction unlinkability, and network anonymity. Then make a comparative analysis on privacy of Bitcoin, Dash, Monero, Verge, Zcash, and Grin from these privacy metrics. Finally, open challenges and future directions on blockchain based privacy cryptocurrencies are discussed. In the future, multi-level privacy enhancement schemes can be combined in privacy cryptocurrencies to improve privacy, performance and scalability.