Financial fraud is an issue with far reaching consequences in the finance industry, government, corporate sectors, and for ordinary consumers. Increasing dependence on new technologies such as cloud and mobile computing in recent years has compounded the problem. Traditional methods involving manual detection are not only time consuming, expensive and inaccurate, but in the age of big data they are also impractical. Not surprisingly, financial institutions have turned to automated processes using statistical and computational methods. This paper presents a comprehensive review of financial fraud detection research using such data mining methods, with a particular focus on computational intelligence (CI)-based techniques. Over fifty scientific literature, primarily spanning the period 2004'2014, were analysed in this study; literature that reported empirical studies focussing specifically on CI-based financial fraud detection were considered in particular. Research gap was identified as none of the existing review articles addresses the association among fraud types, CI-based detection algorithms and their performance, as reported in the literature. We have presented a comprehensive classification as well as analysis of existing fraud detection literature based on key aspects such as detection algorithm used, fraud type investigated, and performance of the detection methods for specific financial fraud types. Some of the key issues and challenges associated with the current practices and potential future direction of research have also been identified.