Privacy is supreme in cryptocurrencies since most users do not want to reveal their identities or the transaction amount in financial transactions. Nevertheless, achieving privacy in blockchain-based cryptocurrencies remains challenging since blockchain is by default a public ledger. For instance, Bitcoin provides built-in pseudonymity rather than true anonymity, which can be compromised by ... [Show full abstract] analyzing the transactions. Several solutions have been proposed to enhance the transaction privacy of Bitcoin. Unfortunately, full anonymity is not always desirable, because malicious users are able to conduct illegal transactions, such as money laundering and drug trading, under the cover of anonymity in cryptocurrencies. As a result, regulation in blockchain-based cryptocurrencies is very essential. In this article, we analyze the privacy issues in Bitcoin and investigate some existing privacy-enhancing techniques in blockchain-based cryptocurrencies as well as some privacy-focused altcoins. In addition, we review and compare some works dealing with regulation of cryptocurrencies. Finally, we propose two possible solutions from a top view to balance privacy and regulation of blockchain-based cryptocurrencies. One solution is based on decentralized group signature, in which a group manager is responsible for building a group and tracing the real payer of the group in a transaction. The other solution is based on verifiable encryption, in which a tracing manager is not actively involved in normal transactions but can trace suspicious transactions via an encrypted tag.