Cryptocurrencies gain trust in users by publicly disclosing the full creation and transaction history. In return, the transaction history faithfully records the whole spectrum of cryptocurrency user behaviors. This article analyzes and summarizes the existing research on knowledge discovery in the cryptocurrency transactions using data mining techniques. Specifically, we classify the existing research into three aspects, i.e., transaction tracings and blockchain address linking, the analyses of collective user behaviors, and the study of individual user behaviors. For each aspect, we present the problems, summarize the methodologies, and discuss major findings in the literature. Furthermore, an enumeration of transaction data parsing and visualization tools and services is also provided. Finally, we outline several future directions in this research area, such as the current rapid development of Decentralized Finance (De-Fi) and digital fiat money.