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The increasing number of credit card fraud cases has become a considerable problem since the past decades. This phenomenon is due to the expansion of new technologies, including the increased popularity and volume of online banking transactions and e-commerce. In order to address the problem of credit card fraud detection, a rule-based approach has been widely utilized to detect and guard against fraudulent activities. However, it requires huge computational power and high complexity in defining and building the rule base for pattern matching, in order to precisely identifying the fraud patterns. In addition, it does not come with intelligence and ability in predicting or analysing transaction data in looking for new fraud patterns and strategies. As such, Data Mining and Machine Learning algorithms are proposed to overcome the shortcomings in this paper. The aim of this paper is to highlight the important techniques and methodologies that are employed in fraud detection, while at the same time focusing on the existing literature. Methods such as Artificial Neural Networks (ANNs), Support Vector Machines (SVMs), naïve Bayesian, k-Nearest Neighbour (k-NN), Decision Tree and Frequent Pattern Mining algorithms are reviewed and evaluated for their performance in detecting fraudulent transaction.